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: Ferreira, R., Groisman, P., Rossi, J.D.
Formato: JOUR
Materias:
Nonlinear boundary conditions
Numerical blow-up
Porous medium equation
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_02182025_v12_n4_p461_Ferreira
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id todo:paper_02182025_v12_n4_p461_Ferreira
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spelling todo:paper_02182025_v12_n4_p461_Ferreira2023-10-03T15:10:48Z Numerical blow-up for a nonlinear problem with a nonlinear boundary condition Ferreira, R. Groisman, P. Rossi, J.D. 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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar 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
Ferreira, R.
Groisman, P.
Rossi, J.D.
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.
format JOUR
author Ferreira, R.
Groisman, P.
Rossi, J.D.
author_facet Ferreira, R.
Groisman, P.
Rossi, J.D.
author_sort Ferreira, R.
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
url http://hdl.handle.net/20.500.12110/paper_02182025_v12_n4_p461_Ferreira
work_keys_str_mv AT ferreirar numericalblowupforanonlinearproblemwithanonlinearboundarycondition
AT groismanp numericalblowupforanonlinearproblemwithanonlinearboundarycondition
AT rossijd numericalblowupforanonlinearproblemwithanonlinearboundarycondition
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