RESEARCH GROUP ON DIFFERENTIAL EQUATIONS AND NUMERICAL ANALYSIS

 

Our group is devoted to the study of partial differential equations and systems of interest in combustion theory, fluid mechanics or in general, reaction diffusion processes. We study these systems from a theoretical point of view. We also propose and analyze new numerical schemes for the approximation of the solutions. Moreover, we compare some of the usual numerical models with the continuous ones looking for blow up of solutions, spurious steady states, equilibrium of steady states and other geometrical properties of the systems under consideration. Moreover, we are interested in the numerical approximation of singular problems (problems which develop a boundary layer or stated in domains with cusps) which brings up the problem of a priori estamates in domains with cusps. 

INTERESTS

PARTICIPANTS

GRANTS

RECENT PUBLICATIONS

 

Some of our present interests are:

a) Free boundary problems of interest in combustion

b) Blow up problems for equations and systems

c) Elliptic systems coupled on the boundary

d) A priori estimates and Sobolev estimates in domains with cusps.

e) Error estimates and adaptivity in numerical methods, in particular for blow up, convection - diffusion and eigenvalue problems. 

f) Numerical approximation for stochastic differential equations.

g) Shape optmization problems related to Sobolev type inequalities. 

h) Comparison of geometric properties of differential equations and their numerical approximations.

i) Poincare and Korn type inequalities in Sobolev spaces with weights.

 

 

PARTICIPANTS

Gabriel Acosta, University of  General Sarmiento and University of Buenos Aires

Maria Gabriela Armentano, University of Buenos Aires 

Leandro del Pezzo, University of Buenos Aires - Under a fellowship of CONICET

Julian Fernández Bonder, University of Buenos Aires 

Irene Drelichman, University of Buenos Aires - Under a fellowship of CONICET

Ricardo G. Durán,  University of Buenos Aires     

Pablo Groisman, University of Buenos Aires

Claudia Lederman, University of Buenos Aires  

Ariel Lombardi, University of Buenos Aires

Fernando López García, University of Buenos Aires. - Under a fellowship of CONICET

Sandra Martínez, University of Buenos Aires - Under a fellowship of CONICET

Juan Pablo Pinasco, University of General Sarmiento and University of Buenos Aires

Mariana Prieto, University of Buenos Aires - Under a fellowship of ANPCYT

Julio D. Rossi , University of Buenos Aires

Nicolas Saintier, University of Buenos Aires - Under a postdoctoral fellowship of ANPCYT

Noemi Wolanski, University of Buenos Aires

 

Associated participants  

Claudio Padra, Centro Atomico Bariloche, CNEA.

Pedro Morin, Universidad Nacional del  Litoral.

Marisa Toschi, University of La Plata - Under a fellowship of CONICET

 

 

GRANTS

Agencia Nacional de Investigaciones Cientificas y Tecnologicas de Argentina, PICT 03-13719, October 2004-September 2007.

UBA, (Projects X052 and X066), January 2004-December 2006.

CONICET, PIP 5478/1438, October 2005-September2007.

 

 

RECENT PUBLICATIONS  

  In Scientific Journals:  (Submitted) (In press) (2006) (2005) (2004) (2003) (2002) (2001) (2000) (1999) (1998)

  In Proceedings

  Surveys  

 

 

Papers submitted for publication:

1. G. Acosta, M. Graña and J. P. Pinasco, Condition Numbers and Scale Free Graphs.

2. F. Andreu - J. M. Mazon - J. D. Rossi - J. Toledo. The Neumann problem for nonlocal nonlinear diffusion equations.  Click

3. María G. Armentano and Claudio Padra, A posteriori error estimates for the Steklov eigenvalue problem.  

4. J. M. Arrieta - A. Rodriguez-Bernal - J. D. Rossi. The best Sobolev trace constant as limit of the usual Sobolev constant for small strips near the boundary Click

5. M. Bogoya - R. Ferreira - J. D. Rossi. A nonlocal nonlinear diffusion equation with blowing up boundary conditions

6. D. Carando, R. Fraiman, P. Groisman, A tailor-made nonparametric density estimate

7. M. Chaves - J. D. Rossi. Regularity results for the blow-up time as a function of the initial data. Click

8. C. Cortazar, M. Elgueta, J. D. Rossi. The blow-up problem for a semilinear parabolic equation with a potential. Click

9. P. L. de Nápoli and J. P. Pinasco,  Estimates for Eigenvalues of Quasilinear Elliptic Systems.

10. R. G. Durán and A. L. Lombardi, Error estimates for the Raviart-Thomas interpolation under the maximum angle condition.

11. J. Fernández Bonder, P. Groisman y J.D. Rossi. Continuity of the explosion time in stochastic differential equations.

12. J. Fernández Bonder, R. Orive y J.D. Rossi. The best Sobolev trace constant in domains with holes for critical or subcritical exponents .

13. J. Fernández Bonder y J.P. Pinasco. Estimates for eigenvalues of quasilinear elliptic systems. Part II.

14. J. Garcia-Melian - J. D. Rossi - J. Sabina. Semilinear problems perturbed through the boundary condition. Click

15. J. García-Melián - J. D. Rossi - J. Sabina. Large solutions to the $p$-Laplacian for large~$p$.  Click

16. J. García-Melián - J. D. Rossi - A. Suárez. The competition between incoming and outgoing fluxes in an elliptic problem.  Click

17. J. García-Melián - C. Morales-Rodrigo - J. D. Rossi - A. Suárez.  Nonnegative solutions to an elliptic problem with nonlinear absorption and a nonlinear incoming flux on the boundary.. Click  

18. M. Graña, J. P. Pinasco, Discrete Scale Invariance in Scale Free Graphs.

19. P. Groisman - J. D. Rossi. The explosion time in stochastic differential equations with small diffusion. Submitted. Click

20. S. Martinez,  J. D. Rossi. On the Fucik spectrum and a resonance problem for the p-Laplacian with a nonlinear boundary condition. . Click

21. S. Martínez, N. Wolanski, A minimization problem with free boundary in Orlicz spaces.

22.  J. P. Pinasco,  Yet Another Proof of the Infinitude of Prime Numbers. 

23.  J. P. Pinasco,  Comparison of Eigenvalues for the p-Laplacian with Integral Inequalities.

24.  J. P. Pinasco,  The Distribution of Non-Principal Eigenvalues of Singular Second Order Linear Ordinary Differential Equations..

25. J. D. Rossi. An estimate for the blow-up time in terms of the initial data.  Click

 

In Press:

1. G. Acosta, M. G. Armentano, R. G. Durán and A. L. Lombardi, Finite element approximations in a non-Lipschitz domain. To appear in SIAM J. Numer. Anal.

2. M. Bogoya - R. Ferreira - J. D. Rossi. Neumann boundary conditions for a nonlocal nonlinear diffusion operator. Continuous and discrete models. To appear in Proceedings of the American Mathematical Society. Click

3. C. Brandle - F. Quiros - J. D. Rossi. An adaptive numerical method to handle blow-up in a parabolic system. To appear in Numerische Mathematik. Click  

4. E. Chasseigne - M. Chaves - J. D. Rossi. Asymptotic behavior for nonlocal diffusion equations.  To appear in Journal de Mathematiques Pures et Appliquees.  Click  

5. C. Cortazar, M. Elgueta, J. D. Rossi, N. Wolanski, Boundary fluxes for non-local diffusion, to appear in J. Diff. Eqs. cerw1.pdf

6. C. Cortázar, M. Elgueta, J. D. Rossi, N. Wolanski, How to approximate the heat equation with Neumann boundary conditions by nonlocal diffusion problems, to appear in Arch. Rat. Mech. Anal.  cerw2.pdf

7. P. L. de Nápoli and J. P. Pinasco,  Eigenvalues of the p-Laplacian and Disconjugacy Criteria. to appear in Jour. of inequalities and applications.

8. P. L. de Nápoli and J. P. Pinasco, Estimates for Eigenvalues of Quasilinear Elliptic Systems, to appear in Jour. Diff. Eqs.

9. J. Fernández Bonder, P. Groisman y J.D. Rossi. Optimization of the first Steklov eigenvalue in domains with holes: A shape derivative approach. to appear in Ann. Mat. Pura Appl.

10. J. Fernandez Bonder, S. Martinez, J. D. Rossi. Existence results for gradient elliptic systems with nonlinear boundary conditions, por aparecer en NODEA Nonlinear Differential Equations and Applications  Click  

11. J. Fernández Bonder, R. Orive y J.D. Rossi. The best Sobolev trace constant in a domain with oscillating boundary. to appear in Nonlinear Anal. TMA.

12. R. Ferreira, F. Quiros, J. D. Rossi, The balance between nonlinear inwards and outwards boundary-flux for a nonlinear heat equation, to appear in Journal of Diff. Eqs. Click  

13. J. García-Azorero,  J. J. Manfredi, I. Peral, J. D. Rossi,  The Neumann problem for the $\infty$-Laplacian and the Monge-Kantorovich mass transfer problem. .To appear in Nonlinear Analysis TM&A Click  

14. J. Garcia-Melian - J. D. Rossi - J. Sabina. A bifurcation problem governed by the boundary condition, por aparecer en Nonlinear Differential Equations and Applications. NoDEA  Click  

15. J. Garcia-Melian - J. D. Rossi - J. Sabina. A bifurcation problem governed by the boundary condition II.  To appear in Proceedings of the London Mathematical Society. Click  

16. C. Lederman, N. Wolanski, A local monotonicity formula for an inhomogeneous singular perturbation problem and applications, to appear in Annali di Matematica Pura Appl. lwannali.pdf

17. C. Lederman, N. Wolanski, A two phase elliptic singular perturbation problem with a forcing term,  to appear in Journal de Math.  Purées Appliqués. nonlocal-elliptic.pdf:

18. J. P. Pinasco,  Asymptotic of eigenvalues of the p-Laplace operator and lattice points, por aparecer en Acta Math. Sinica.

19. J. P. Pinasco,  The Asymptotic behavior of Nonlinear Eigenvalues, to appear in Rocky Mountain J. of Math. 

20. J. P. Pinasco,  The Distribution of Non-Principal Eigenvalues of Singular Second Order Linear Ordinary Differential Equations, to appear in International Jour. of Math. and Mathematical Sciences.

21. J. D. Rossi,  First variations of the best Sobolev trace constant with respect to the domain. To appear in Canadian Mathematical Bulletin. Click

22. J. D. Rossi - M. Saez. Optimal regularity for the pseudo infinity Laplacian. To appear in ESAIM. Control, Optimisation and Calculus of Variations. Click

     

2006

1. G. Acosta, R. G. Durán and A. L. Lombardi, Weighted Poincaré and Korn inequalities for Hölder domains,  Math. Meth. Appl. Sci..29 (4), 387-400, 2006.  poscript file

2. G. Acosta, R. G. Durán and M. A. Muschietti, Solutions of the divergence operator on John domains. Advances in Mathematics, 206(2), 373-401, 2006 postcript file 

3. C. Brandle - F. Quiros - J. D. Rossi.  A complete classification of simultaneous blow-up rates. Applied Mathematics Letters. Vol. 19(7), 607-611, (2006). Click

4. L. Del Pezzo y J. Fernández Bonder. An optimization problem for the first eigenvalue of the p-Laplacian plus a potential. Comm. Pure Appl. Anal. 5 (2006), no. 4, pp. 675--690.

5. L. Del Pezzo, J. Fernández Bonder y J.D. Rossi. An optimization problem for the first Steklov eigenvalue of a nonlinear problem. Differential Integral Equations, 19 (2006), no. 9, 1035--1046.

6. R. G. Durán, Ariel L. Lombardi, Finite element approximation of convection diffusion problems using graded meshes, Applied Numerical Mathematics 56, 1314-1325, 2006.

7. J. Fernández Bonder, Multiple solutions for the p-laplace equation with nonlinear boundary conditions, Electronic. Jour. Diff. Eqs. 2006(2006), 37, 1-7.  

8. J. Fernández Bonder, S. Martínez, N. Wolanski,  An optimization problem with a volume constrain for a degenerate quasilinear operator,  Jour. Diff. Eqs. 227(1), 2006, 80–101. opt-p-laplace.pdf.  

9. J. Fernández Bonder, J. D. Rossi, N. Wolanski,  On the best Sobolev trace constant and extremals in domains with holes,  Bulletin des Sciences Mathematique.30, 2006, 565–579.. hole1.pdf  

10. R. Ferreira - A. de Pablo - J. D. Rossi. Blow-up for a degenerate diffusion problem not in divergence form, Indiana University Mathematics Journal.  55(3), 955-974, (2006).    Click  

11. R. Ferreira, A. de Pablo, F. Quiros, J. D. Rossi. Non-simultaneous quenching in a system of heat equations coupled at the boundary,  Zeitschrift fur Angewandte Mathematik und Physik 57(4), 586-594, (2006). Click

12. J. Garcia-Azorero - J. J. Manfredi - I. Peral - J. D. Rossi. Steklov eigenvalues for the $\infty$-Laplacian.  Rendiconti Lincei Matematica e Applicazioni. Vol. 17(3), 199-210, (2006). Click  

13. P. Groisman, Totally discrete explicit and semi-implicit Euler methods for a blow-up problem in several space dimensions, Computing  76 ( 3-4), (2006),   325--352.

14. C. Lederman, N. Wolanski, Singular perturbation in a nonlocal diffusion model,  Communications in PDE 31(2), 2006, 195–241  nolo1.pdf  

 

2005:

1. G. Acosta, M. A. Armentano, R. G. Durán, A. L. Lombardi, Nonhomogeneous Neumann problem for the Poisson equation in domains with an external cusp, J. Math. Anal. Appl. 310 (2), 397-411, (2005). pdf file 

2. C. Brandle - F. Quiros - J. D. Rossi. Non-simultaneous blow-up for a quasilinear parabolic system with reaction at the boundary. Communications on Pure and Applied Analysis. Vol 4(3), 523-536, (2005). Click

3. C. Brandle - F. Quiros - J. D. Rossi. The role of nonlinear diffusion in non-simultaneous blow-up. Journal of Mathematical Analysis and Applications. Vol. 308(1), 92-104, (2005). Click

4. C. Cortazar - M. Elgueta - J. D. Rossi. A non-local diffusion equation whose solutions develop a free boundary,  Nonlinear Analysis Ann. Inst. Henri Poincaré Vol 6(2), 269-281, (2005). Click .

5. J. Davila, J. Fernandez Bonder, P. Groisman, J.D. Rossi and M. Sued. Numerical Analysis of Stochastic Differential Equations with Explosions,  Stochastic Analysis and Applications. 23 (4) 809--826 (2005).  

6. P. L. de Nápoli and J. P. Pinasco,  A Lyapunov inequality for monotone quasilinear operators,   Differential and Integral Equations 18 (10) (2005) 1193-1200. 

7. R. G. Durán and A. L. Lombardi, Error estimates on anisotropic Q1 elements for functions in weighted Sobolev spaces, Math. Comp. 74, 1679-1706, 2005. postcript file

8. J. Fernández Bonder, J.P. Pinasco. Eigenvalues of the p-laplacian in fractal strings with indefinite weights.,  Jour. Math. Anal. Appl. 388, 2005, 764-774. 

9. J. Fernandez Bonder – J. D. Rossi. On the existence of extremals for the Sobolev trace embedding theorem with critical exponent. Bulletin of the London Mathematical Society Vol. 37 (1), 119-125, (2005).    

10.  J. Fernández  Bonder, J. D. Rossi, N. Wolanski, Regularity of the free boundary in an optimization problem related to the best Sobolev trace constant,  SIAM Jour. Control and Optimization 44(5), 2005, 1612–1635.   hole2.pdf

11. Julian Fernandez Bonder and Juan P. Pinasco,  Eigenvalues of the p-laplacian in fractal strings with indefinite weights,  Journal of Mathematical Analysis and Applications. 308 (2005) 764-774. 

12. R. Ferreira – A. de Pablo – F. Quiros – J. D. Rossi. On the quenching set for a fast diffusion equation. Regional quenching. Proccedings of the Royal Society of Edimburgh Vol. 135A, 585-601, (2005)..Click  

13. Juan P. Pinasco and Julio D. Rossi,  Asymptotics of the spectral function for the Steklov problem in a family of sets with fractal boundaries,  Applied Mathematics E-Notes. 5 (2005) 138-146 

14. Juan P. Pinasco,  On the Asymptotic Behavior of Eigenvalues of the Radial p-laplacian, . Manuscripta Mathematica, 117 (3) (2005) 363-371.

15. J. D. Rossi - P. Souplet. Coexistence of simultaneous and non simultaneous blow-up in a semilinear parabolic system, Differential and Integral Equations Vol. 18 (4), 405-418, (2005).

 

2004:

1. F. Andreu - J. M. Mazon - J. D. Rossi. The best constant for the Sobolev trace embedding from W^1,1(W) into L¹(¶W),  Nonlinear Analysis TM&A. Vol. 59 (7), 1125-1145, (2004). Click

2. D. Arcoya - J. D. Rossi. Antimaximum principle  for quasilinear problems, Advances in Differential Equations. Vol. 9 (9&10), 1185-1200, (2004). Click

3. María G. Armentano, The effect of reduced integration in the Steklov eigenvalue problem, Mathematical Modelling and Numerical Analysis (M2AN), vol 38, no 1, pp 27-36 (2004).

4. M. G. Armentano  and R. G. Durán, Asymptotic lower bounds for eigenvalues by nonconforming finite element methods. Electronic Trans. Numer. Anal. 17, 93-101, 2004. postcript file

5. C. Brandle - P. Groisman - J. D. Rossi.  Fully discrete adaptive methods for a blow-up problem, Mathematical Models and Methods in the Applied Sciences, M3AS Vol. 14 (10), 1425-1450, (2004). Click

6. M. Chaves, J. D. Rossi, Regularity results for the blow-up time as a function of the initial data. Differential and Integral Equations. Vol. 17 (11&12), 1263-1271, (2004). Click

7. J. Davila - J. D. Rossi. Self-similar solutions of the porous medium equation in a half-space with a nonlinear boundary condition. Existence and symmetry, Journal of Mathematical Analysis and Applications Vol. 296, 634-649, (2004). Click

8. R. G. Durán and M. A. Muschietti, The Korn inequality for Jones domains, Electronic Jour. Diff. Eqs. Vol. 2004(2004), No. 127, pp. 1-10. postcript file 

9. Fernández Bonder, Multiple positive solutions for quasilinear elliptic problems with sign-changing nonlinearities,   Abstr. Appl.Anal. 2004 (2004), no. 12, 1047--1056.

10. J. Fernández Bonder – E. Lami Dozo – J. D. Rossi. Symmetry properties for the extremals of the Sobolev trace embedding, Annales de l'Institut Henri Poincare. Analyse Non Lineaire Vol. 21 (6), 795-805, (2004).. Click

11. J. Fernandez Bonder - S. Martinez - J. D. Rossi. The behaviour of the best Sobolev trace constant and extremals in thin domains. Journal of Differential Equations. Vol. 198 (1), 129-148, (2004). Click

12. J. Fernández Bonder, N. Wolanski. Uniqueness of limit solutions for a free boundary problem from combustion. SIAM Journal on Mathematical Analysis, 36 (2004), no. 1, 172-185.

13. R. Ferreira - A. de Pablo - F. Quiros - J. D. Rossi. Superfast quenching.  Journal of Differential Equations. Vol. 199 (1), 189-209, (2004). Click

14. R. Ferreira – P. Groisman – J. D. Rossi. Numerical blow-up for the porous medium equation with a source. Numerical Methods for Partial Differential Equations. Vol 20 (4), 552-575, (2004). Click

15. J. Garcia Azorero - I. Peral - J. D. Rossi. A convex-concave problem with a nonlinear boundary condition. Journal of Differential Equations. Vol. 198 (1), 91-128, (2004).

16. J. Garcia-Melian - J. D. Rossi.  Boundary blow-up solutions to elliptic systems of competitive type, Journal of Differential Equations Vol. 206 (1), 156-181, (2004) Click

17. P. Groisman – J. D. Rossi. Dependence of the blow-up time with respect to parameters and numerical approximations for a parabolic problem. Asymptotic Analysis.  Vol. 37 (1), 79-91, (2004) . Click

18. C. Lederman, J. M. Roquejoffre, N. Wolanski, Mathematical justification of a nonlinear integro-differential equation for the propagation of spherical flames,  Annali di Matematica Pura ed Applicata  183, 173–239 (2004)   (Resumen aparecido en Compt Rendu Acad. Sci. Series I Mathematics 334(7), 569-574, 2002. )

19. S. Martinez,  J. D. Rossi. On the Fucik spectrum and a resonance problem for the p-Laplacian with a nonlinear boundary condition.  Nonlinear Analysis TM&A. Vol. 59 (6), 813-848, (2004). Click

20. J. P. Pinasco , Lower bounds for eigenvalues of the one-dimensional p-Laplacian, Abstract and Applied Analysis, Vol (2004) 147-153

21. Juan P. Pinasco,  Lower bounds of Fucik eigenvalues of the weighted one dimensional p-Laplacian,  Rendiconti dell'Istituto Matematico dell'Universita' di Trieste XXXVI (2004) 1-16.

22. F. Quiros – J. D. Rossi. Blow-up sets for linear diffusion equations in one dimension. Zeitschrift fur Angewandte Mathematik und Physik. Vol. 55 (2), 357-362, (2004). Click

23. F. Quiros - J. D. Rossi - J. L. Vazquez. Thermal avalanche for blow-up solutions of semilinear heat equations. Communications on Pure and Applied Mathematics. Vol. LVII, No. 1, 59-98, (2004). Click

2003:

1. G. Acosta and R. G. Durán, An optimal Poincaré inequality in L¹ for convex domains, Proc. AMS 132(1), 195-202, 2003. postcript file

2. M. G. Armentano and R. G. Durán, Mass lumping or not mass lumping in eigenvalue problems, Numerical Methods for Partial Differential Equations 19(5), 2003, 653--664.

3. C. Cortazar - M. Elgueta - J. D. Rossi. Uniqueness and non-uniqueness for the porous medium equation with non linear boundaryonditions.  Differential and Integral Equations Vol. 16, No. 10, 1215-1222, (2003). Click  

4. R. G. Durán, E. Hernández,  L. Hervella Nieto, E. Liberman and R. Rodríguez, Error estimates for low-order isoparametric quadrilateral finite elements for plates. SIAM J. Numer. Anal. 41(5), 1751-1772, 2003. pdf file

5. R. G. Durán, C. Padra and R. Rodríguez, A posteriori error estimates for the finite element approximation of eigenvalue problems. Math. Mod. Meth. Appl. Sci. 13(8), 1219-1229, 2003. postcript file

6. J. Fernandez Bonder - R. Ferreira - J. D. Rossi. Uniform bounds for the best Sobolev trace constant. Advanced Nonlinear Studies. Vol. 3 (2), 181-192, (2003). Click

7. J. Fernández Bonder, J.P. Pinasco. Asymptotic behavior of the eigenvalues of the one dimensional weighted p-laplace operator. Ark Mat, 41 (2003), 267--280.

8. R. Ferreira - A. de Pablo - F. Quiros - J. D. Rossi. The blow-up profile for a fast diffusion equation with a nonlinear boundary condition.  Rocky Mountain Journal of Mathematics 33 (1), 123-146, (2003).. Click  

9. R. Ferreira – P. Groisman – J. D. Rossi. An adaptive numerical scheme for a parabolic problem with blow-up. IMA Journal of Numerical Analysis.  Vol. 23 (3), 439-463, (2003). Click 

10. P. Groisman – J. D. Rossi – H. Zaag. On the dependence of the blow-up time with respect to the initial data in a semilinear  parabolic problem. Communications in Partial Differential Equations. Vol. 28 (3\&4), 737-744, (2003). Click

11. S. Martinez - J. D. Rossi. Weak solutions for the p-Laplacian with a nonlinear boundary condition at resonance. Electronic Journal of Differential Equations. Vol. 2003, No 27, 1-14, (2003). Click

12. F. Quiros – J. D. Rossi. Non-simultaneous blow-up in a nonlinear parabolic system. Advanced Nonlinear Studies. Vol. 3(3), 397-418, (2003). Click

2002: 

1. G. Acosta, J. Fernández Bonder, P. Groisman, J. D. Rossi, Simultaneous vs. non-simultaneous blow up in numerical approximations of a parabolic system with nonlinear boundary conditions, M2AN Math. Model. Numer. Anal. 36(1), 55-68, 2002.  Click.

2. G. Acosta, J. Fernández Bonder, P. Groisman, J. D. Rossi, Numerical approximation of a parabolic problem with a nonlinear boundary condition in several space dimensions, Discrete and continuous dynamical systems - serie B 2(2), 279-294, 2002. Click

3. G. Acosta, R. G. Durán, J. D. Rossi, An adaptive time step procedure for a parabolic problem with blow up, Computing 68(4), 343-373, 2002. postcript file

4. F. Andreu - J. M. Mazon - J. Toledo - J. D. Rossi,  Porous medium equation with absorption and a nonlinear boundary condition, Nonlinear Analysis TM&A. 49(4), 541-563, 2002. Click  

5. J. Carrillo, C. Lederman, P. A. Markowich, G. Toscani, Poincare inequalities for linearizations of very fast diffusion equations, Nonlinearity 15, 565-580, 2002.

6. C. Cortazar - M. Elgueta - J. D. Rossi. Short time behavior near the boundary for the heat equation with a nonlinear boundary condition, Nonlinear Analysis TM&A. 50, 205-213, 2002.  Click  

7. A. de Pablo - F. Quiros - J. D. Rossi. Non-simultaneous quenching, Applied Math. Letters 15, 265-269, 2002. Click  

8. A. de Pablo - F. Quiros - J. D. Rossi. Asymptotic simplification for a reaction diffusion problem with a nonlinear boundary condition, IMA Jour. Appl. Math. 67, 69-98, 2002. Click  

9. J. Fernández Bonder - P. Groisman - J. D. Rossi. On numerical blow-up sets, Proc. Amer. Math. Soc. 130(7), 2049-2055, 2002. Click  

10. J. Fernández Bonder, J. D. Rossi. Life span for solutions of the heat equations with a nonlinear boundary condition, Tsukuba J. Math. 25(1), 215-220, 2002.

11. J. Fernández Bonder, J. D. Rossi. A fourth order elliptic equation with nonlinear boundary  conditions,  Nonlinear Anal. TM&A 49(8), 1037-1047, 2002. 

12. J. Fernández Bonder, J. D. Rossi, A nonlinear eigenvalue problem with indefinite weights related to the Sobolev trace embedding, Publ. Mat. 46, 221-235, 2002.  Click

13. J. Fernández Bonder, J.D. Rossi. Asymptotic behavior of the best Sobolev trace constant in expanding and contracting domains. Comm. Pure Appl. Anal. 1 (2002), no. 3, 359--378.

14. R. Ferreira – P. Groisman – J. D. Rossi. Numerical blow-up for a nonlinear problem with a nonlinear boundary condition, Mathematical Models and Methods in the Applied Sciences 12(4), 461-484, 2002. Click  

15. C. Lederman, P. A. Markowich, On fast-diffusion equations with infinite equilibrium entropy and finite equilibrium mass,  Comm. Partial. Diff. Eqs. 28 (1&2) (2003), 301-332.

16. S. Martinez, J. D. Rossi, Isolation and simplicity for the first eigenvalue of the p-laplacian with a nonlinear boundary condition, Abstract and Applied Analysis 7(5), 287-293, 2002.

17. F. Quiros - J. D. Rossi - J. L. Vazquez. Complete blow-up and thermal avalanche for  heat equations with nonlinear boundary conditions, Communications in Partial Differential Equations 27(1&2), 395-424, 2002. Click  

2001:

1. G. Acosta, Lagrange and average interpolation over 3D anisotropic elements, Jour. on Comp. and Applied Math. 135, 2001, 91-109.

2. M. G. Armentano, Error estimates in Sobolev spaces for moving least square approximations,  SIAM Jour. Numer. Anal. 39(1), 2001, 38-51. postcript file

3. M. G. Armentano and R. G. Durán, Error estimates for moving least square approximations, Applied  Numerical  Mathematics, 37, 397-416,  2001. postcript file

4. G. C. Buscaglia, R. G. Durán, E. A. Fancello,R. A. Feijóo  and C. Padra, An adaptive finite element approach for frictionless contact problems,  Int. J. Numer. Meth. Engng.  50, 395-418,  2001.  postcript file

5. R. G. Durán and M. A. Muschietti, On the traces of  W^2,p for a Lipschitz domain, Revista Matemática Complutense XIV(2),  371-377, 2001.  postcript file

6. R. G. Durán and M. A. Muschietti,  An explicit right inverse of the divergence operator which is continuous in weighted   norms, Studia Mathematica  148(3), 207-219, 2001.  postcript file

7. J. Fernández Bonder, J. D. Rossi. Blow-up vs. spurious steady solutions. Proc. Amer. Math. Soc., 129 (1) (2001), pp. 139-144.       

8. J. Fernández Bonder, J. D. Rossi. Existence for an elliptic system with nonlinear boundary   conditions via fixed point methods. Advances Differential Equations, 6 (1) (2001), pp. 1-20.

9. J. Fernández Bonder, J. D. Rossi. Existence results for the p-Laplacian with nonlinear boundary  conditions,  J. Math. Anal. Appl. 263, 195-233, 2001. 

10. P. Groisman - J. D. Rossi, Asymptotic behaviour for a numerical approximation of a parabolic problem with blowing up solutions, Journal of Computational and Applied Mathematics 135, 135-155, 2001.. Click  

11. C. Lederman, J. L. Vázquez and N. Wolanski, Uniqueness of solution to a free boundary problem from combustion,  Trans. AMS. 353(2), 2001, 655-692.

12.   C. Lederman, J. L. Vázquez and N. Wolanski, A mixed semilinear parabolic problem in a non-cylindrical space-time domain, Diff. Int. Eqs. 14(4), 2001, 385-404.

13. C. Lederman, J. L. Vázquez and N. Wolanski, Uniqueness in a two phase free boundary problem, Advances in Diff. Eqs. 6(12), 2001, 1409-1442.

14. F. Quiros - J. D. Rossi,. Non simultaneous blow-up in a semilinear parabolic system. Zeitschrift fur Angewandte Mathematik und Physik.Vol. 52 (2), 342-346, (2001). Click  

15. F. Quiros - J. D. Rossi, Blow-up sets and Fujita type curves for a degenerate parabolic system with nonlinear boundary conditions,  Indiana University Mathematics Journal 50(1), 629-654, 2001. Click  

2000:

1. G. Acosta, J. Fernández Bonder, J. D. Rossi. Stable manifold approximation for the heat equation with nonlinear boundary conditions. J. Dynam. Differential Equations, 12 (3) (2000), pp. 557-578.

2. G. Acosta  and R. G. Durán , The maximum angle condition for mixed and non conforming elements: Application to the Stokes equations,  SIAM J. Numer. Anal.  37, 18-36, 2000.  postcript file 

3. G. Acosta and R. G. Durán, Error estimates for $Q_1$ isoparametric elementssatisfying a weak angle condition, SIAM J. Numer. Anal. 38, 1073-1088,  2000. A. Bermúdez, R. G. Durán, R. Rodríguez and J. Solomín, Finite element analysis of a quadratic eigenvalue problem arising in dissipative acoustics,  SIAM J. Numer. Anal.  38,  267-291,  2000.  postcript file

4. E. Dari , R. G. Durán and C. Padra,  Maximum norm error estimators for three dimensional elliptic problems, SIAM J. Numer. Anal. 37(2), 683-700,  2000.  postcript file 

5. R. G. Durán, L. Hervella Nieto, E. Liberman, R. Rodríguez and J. Solomin,   Finite element analysis of the vibration problem of  a plate coupled with a fluid,  Numer. Math.  86, 591-616, 2000.  postcript file   

6. J. Fernández Bonder and J. D. Rossi, Asymptotic behaviour for a parabolic system with nonlinear boundary conditions. Collect. Math., 51 (3) (2000), pp. 285-308.

7. J. Fernández Bonder and N. Wolanski,  A free boundary problem in combustion, Interfaces and Free Boundaries 2, 2000,   381-411.

8. J. P. Pinasco and J. D. Rossi, Simultaneous vs. non simultaneous blow up, New Zealand Jour. of Math. 29(1), 2000, 55-59. Click

1999:

1. D. Boffi, R. G. Durán and L. Gastaldi, A remark on spurious eigenvalues in a square,   Applied Mathematics Letters  12, 107-114, 1999.  postcript file

2. C. Cortazar, M. Elgueta and J. D. Rossi, Uniqueness and non uniqueness for a system of heat equations with nontrivial coupling at the boundary, Nonlinear Anal. TM&A 37(2), 1999, 257-267.  Click     

3. R. G. Durán, Error estimates for narrow 3-d finite elements, Math. Comp. 68, 187-199, 1999.  postcript file

4. R. G. Durán , L. Gastaldi and C. Padra, A posteriori error estimators for mixed approximations of eigenvalue problems,   Math. Mod. Meth. Appl. Sci.  9, 1165-1178, 1999.  postcript file  

5. R.G. Durán , L. Hervella Nieto, E. Liberman, R. Rodríguez and J. Solomin, Approximation of the vibration modes of a plate by  Reissner-Mindlin equations,  Math. Comp.  68, 1447-1463, 1999.  postcript file  

6. J. Fernandez Bonder, J. P. Pinasco and J. D. Rossi, Existence for a Hamiltonian elliptic system with nonlinear boundary    conditions, Electronic Jour. Diff. Eqs. 40, 1999, 1-15.

7. D. Rial and J. D. Rossi, Localization of blow up points for a parabolic system with a nonlinear boundary condition, Rendiconti del Circolo Matematico di Palermo Serie II, Tomo XLVIII, 1999, 135-152. Click

 

1998:

1. A. Bermúdez,  R. G. Durán  and R. Rodríguez,  Finite element analysis of compressible and incompressible fluid-solid systems,  Math. Comp.  67, 111-136,  1998. postcript file

2. R. G. Durán, J. Etcheverry  and J. D. Rossi, Numerical approximation of a parabolic problem with a nonlinear boundary condition, Discrete and Continuous Dynamical Systems 4(3), 497-506, 1998.  postcript file

3. C. Lederman and N. Wolanski, Viscosity solutions and regularity of the free boundary for the limit of an elliptic two phase singular perturbation problem,  Ann. Scuola Norm. Sup. Pisa. Cl. Sci.(4) 27(2), 1998, 253-288.

4. J. D. Rossi, The blow up rate for a semilinear parabolic equation with a nonlinear boundary condition, Acta Math. Univ. Comenianae 67(2), 1998, 343-350. Click

5. J. D. Rossi and N. Wolanski,  Global existence and nonexistence for a linear system with nonlinear boundary conditions,  Diff. and Int. Eq. 11(1), 1998, 179-190.