Asymptotic behaviour for a numerical approximation of a parabolic problem with blowing up solutions

In this paper, we study the asymptotic behaviour of a semidiscrete numerical approximation for Ut = Uxx + up in a bounded interval, (0, 1), with Dirichlet boundary conditions. We focus in the behaviour of blowing up solutions. We find that the blow-up rate for the numerical scheme is the same as for...

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Autores principales: Groisman, P., Rossi, J.D.
Formato: JOUR
Materias:
Asymptotic behaviour
Blow-up
Semidiscretization in space
Semilinear parabolic equations
Asymptotic stability
Boundary conditions
Semidiscrete numerical approximation
Approximation theory
mathematical analysis
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_03770427_v135_n1_p135_Groisman
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
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spelling todo:paper_03770427_v135_n1_p135_Groisman2023-10-03T15:31:27Z Asymptotic behaviour for a numerical approximation of a parabolic problem with blowing up solutions Groisman, P. Rossi, J.D. Asymptotic behaviour Blow-up Semidiscretization in space Semilinear parabolic equations Asymptotic stability Boundary conditions Semidiscrete numerical approximation Approximation theory mathematical analysis In this paper, we study the asymptotic behaviour of a semidiscrete numerical approximation for Ut = Uxx + up in a bounded interval, (0, 1), with Dirichlet boundary conditions. We focus in the behaviour of blowing up solutions. We find that the blow-up rate for the numerical scheme is the same as for the continuous problem. Also we find the blow-up set for the numerical approximations and prove that it is contained in a neighbourhood of the blow-up set of the continuous problem when the mesh parameter is small enough. © 2001 Elsevier Science B.V. All rights reserved. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_03770427_v135_n1_p135_Groisman
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Asymptotic behaviour
Blow-up
Semidiscretization in space
Semilinear parabolic equations
Asymptotic stability
Boundary conditions
Semidiscrete numerical approximation
Approximation theory
mathematical analysis
spellingShingle Asymptotic behaviour
Blow-up
Semidiscretization in space
Semilinear parabolic equations
Asymptotic stability
Boundary conditions
Semidiscrete numerical approximation
Approximation theory
mathematical analysis
Groisman, P.
Rossi, J.D.
Asymptotic behaviour for a numerical approximation of a parabolic problem with blowing up solutions
topic_facet Asymptotic behaviour
Blow-up
Semidiscretization in space
Semilinear parabolic equations
Asymptotic stability
Boundary conditions
Semidiscrete numerical approximation
Approximation theory
mathematical analysis
description In this paper, we study the asymptotic behaviour of a semidiscrete numerical approximation for Ut = Uxx + up in a bounded interval, (0, 1), with Dirichlet boundary conditions. We focus in the behaviour of blowing up solutions. We find that the blow-up rate for the numerical scheme is the same as for the continuous problem. Also we find the blow-up set for the numerical approximations and prove that it is contained in a neighbourhood of the blow-up set of the continuous problem when the mesh parameter is small enough. © 2001 Elsevier Science B.V. All rights reserved.
format JOUR
author Groisman, P.
Rossi, J.D.
author_facet Groisman, P.
Rossi, J.D.
author_sort Groisman, P.
title Asymptotic behaviour for a numerical approximation of a parabolic problem with blowing up solutions
title_short Asymptotic behaviour for a numerical approximation of a parabolic problem with blowing up solutions
title_full Asymptotic behaviour for a numerical approximation of a parabolic problem with blowing up solutions
title_fullStr Asymptotic behaviour for a numerical approximation of a parabolic problem with blowing up solutions
title_full_unstemmed Asymptotic behaviour for a numerical approximation of a parabolic problem with blowing up solutions
title_sort asymptotic behaviour for a numerical approximation of a parabolic problem with blowing up solutions
url http://hdl.handle.net/20.500.12110/paper_03770427_v135_n1_p135_Groisman
work_keys_str_mv AT groismanp asymptoticbehaviourforanumericalapproximationofaparabolicproblemwithblowingupsolutions
AT rossijd asymptoticbehaviourforanumericalapproximationofaparabolicproblemwithblowingupsolutions
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