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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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 |
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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 |
work_keys_str_mv |
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1807322512872177664 |