Numerical blow-up for a nonlinear problem with a nonlinear boundary condition

In this paper we study numerical approximations for positive solutions of a nonlinear heat equation with a nonlinear boundary condition. We describe in terms of the nonlinearities when solutions of a semidiscretization in space exist globally in time and when they blow up in finite time. We also fin...

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Autores principales: Groisman, Pablo Jose, Rossi, Julio Daniel
Publicado: 2002
Materias:
Nonlinear boundary conditions
Numerical blow-up
Porous medium equation
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_02182025_v12_n4_p461_Ferreira
http://hdl.handle.net/20.500.12110/paper_02182025_v12_n4_p461_Ferreira
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_02182025_v12_n4_p461_Ferreira
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spelling paper:paper_02182025_v12_n4_p461_Ferreira2023-06-08T15:21:22Z Numerical blow-up for a nonlinear problem with a nonlinear boundary condition Groisman, Pablo Jose Rossi, Julio Daniel Nonlinear boundary conditions Numerical blow-up Porous medium equation In this paper we study numerical approximations for positive solutions of a nonlinear heat equation with a nonlinear boundary condition. We describe in terms of the nonlinearities when solutions of a semidiscretization in space exist globally in time and when they blow up in finite time. We also find the blow-up rates and the blow-up sets. In particular we prove that regional blow-up is not reproduced by the numerical scheme. However, in the appropriate variables we can reproduce the correct blow-up set when the mesh parameter goes to zero. Fil:Groisman, P. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Rossi, J.D. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2002 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_02182025_v12_n4_p461_Ferreira http://hdl.handle.net/20.500.12110/paper_02182025_v12_n4_p461_Ferreira
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Nonlinear boundary conditions
Numerical blow-up
Porous medium equation
spellingShingle Nonlinear boundary conditions
Numerical blow-up
Porous medium equation
Groisman, Pablo Jose
Rossi, Julio Daniel
Numerical blow-up for a nonlinear problem with a nonlinear boundary condition
topic_facet Nonlinear boundary conditions
Numerical blow-up
Porous medium equation
description In this paper we study numerical approximations for positive solutions of a nonlinear heat equation with a nonlinear boundary condition. We describe in terms of the nonlinearities when solutions of a semidiscretization in space exist globally in time and when they blow up in finite time. We also find the blow-up rates and the blow-up sets. In particular we prove that regional blow-up is not reproduced by the numerical scheme. However, in the appropriate variables we can reproduce the correct blow-up set when the mesh parameter goes to zero.
author Groisman, Pablo Jose
Rossi, Julio Daniel
author_facet Groisman, Pablo Jose
Rossi, Julio Daniel
author_sort Groisman, Pablo Jose
title Numerical blow-up for a nonlinear problem with a nonlinear boundary condition
title_short Numerical blow-up for a nonlinear problem with a nonlinear boundary condition
title_full Numerical blow-up for a nonlinear problem with a nonlinear boundary condition
title_fullStr Numerical blow-up for a nonlinear problem with a nonlinear boundary condition
title_full_unstemmed Numerical blow-up for a nonlinear problem with a nonlinear boundary condition
title_sort numerical blow-up for a nonlinear problem with a nonlinear boundary condition
publishDate 2002
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_02182025_v12_n4_p461_Ferreira
http://hdl.handle.net/20.500.12110/paper_02182025_v12_n4_p461_Ferreira
work_keys_str_mv AT groismanpablojose numericalblowupforanonlinearproblemwithanonlinearboundarycondition
AT rossijuliodaniel numericalblowupforanonlinearproblemwithanonlinearboundarycondition
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