The balance between nonlinear inwards and outwards boundary flux for a nonlinear heat equation

We study nonnegative solutions of {ut = (um)xx, (x,t)ε(0,L) × (0,T), {-(um)x(0,t) = up(0,t), tε(0,T), {(u,m)x(L,t) = -λuq(L,t), tε(0,T), {u(x,0) = u0(x), xε(0,L), where m, p, q, λ and L are positive parameters. For different values of the parameters three situations may occur: (1) all solutions of t...

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Autores principales: Ferreira, R., Quirós, F., Rossi, J.D.
Formato: JOUR
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_00220396_v184_n1_p259_Ferreira
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id todo:paper_00220396_v184_n1_p259_Ferreira
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spelling todo:paper_00220396_v184_n1_p259_Ferreira2023-10-03T14:25:30Z The balance between nonlinear inwards and outwards boundary flux for a nonlinear heat equation Ferreira, R. Quirós, F. Rossi, J.D. We study nonnegative solutions of {ut = (um)xx, (x,t)ε(0,L) × (0,T), {-(um)x(0,t) = up(0,t), tε(0,T), {(u,m)x(L,t) = -λuq(L,t), tε(0,T), {u(x,0) = u0(x), xε(0,L), where m, p, q, λ and L are positive parameters. For different values of the parameters three situations may occur: (1) all solutions of this problem exist for all t > 0; (2) for certain initial data functions the solution exists for all t > 0 while for others the solution blows up as t ↗ T for some finite T; (3) excepting the trivial solution when u0 ≡ 0, all solutions blow up as t ↗ T for some finite T. We identify in terms of the parameters which of them actually happens. For solutions which blow up we find the blow-up rate and the blow-up set. © 2002 Elsevier Science (USA). JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_00220396_v184_n1_p259_Ferreira
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
description We study nonnegative solutions of {ut = (um)xx, (x,t)ε(0,L) × (0,T), {-(um)x(0,t) = up(0,t), tε(0,T), {(u,m)x(L,t) = -λuq(L,t), tε(0,T), {u(x,0) = u0(x), xε(0,L), where m, p, q, λ and L are positive parameters. For different values of the parameters three situations may occur: (1) all solutions of this problem exist for all t > 0; (2) for certain initial data functions the solution exists for all t > 0 while for others the solution blows up as t ↗ T for some finite T; (3) excepting the trivial solution when u0 ≡ 0, all solutions blow up as t ↗ T for some finite T. We identify in terms of the parameters which of them actually happens. For solutions which blow up we find the blow-up rate and the blow-up set. © 2002 Elsevier Science (USA).
format JOUR
author Ferreira, R.
Quirós, F.
Rossi, J.D.
spellingShingle Ferreira, R.
Quirós, F.
Rossi, J.D.
The balance between nonlinear inwards and outwards boundary flux for a nonlinear heat equation
author_facet Ferreira, R.
Quirós, F.
Rossi, J.D.
author_sort Ferreira, R.
title The balance between nonlinear inwards and outwards boundary flux for a nonlinear heat equation
title_short The balance between nonlinear inwards and outwards boundary flux for a nonlinear heat equation
title_full The balance between nonlinear inwards and outwards boundary flux for a nonlinear heat equation
title_fullStr The balance between nonlinear inwards and outwards boundary flux for a nonlinear heat equation
title_full_unstemmed The balance between nonlinear inwards and outwards boundary flux for a nonlinear heat equation
title_sort balance between nonlinear inwards and outwards boundary flux for a nonlinear heat equation
url http://hdl.handle.net/20.500.12110/paper_00220396_v184_n1_p259_Ferreira
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