1Department of Mathematics Southeast University Nanjing 211189, P.R. China and Department of Mathematics Nantong University Nantong 226019, P.R. China 2School of Mathematics and Physics Changzhou University Changzhou 213164, P.R. China 3Department of Mathematics Nantong University Nantong 226019, P.R. China
Annales Polonici Mathematici, Tome 102 (2011) no. 2, pp. 187-203
This paper deals with blow-up properties of solutions to a semilinear parabolic system with weighted localized terms, subject to the homogeneous Dirichlet boundary conditions. We investigate the influence of the three factors: localized sources $u^p(x_0,t)$, $v^n(x_0,t)$, local sources $u^m(x,t)$, $v^q(x,t)$, and weight functions $a(x), b(x)$, on the asymptotic behavior of solutions. We obtain the uniform blow-up profiles not only for the cases $m, q \leq 1$ or $m, q>1$, but also for $m>1 \mathbin {\}q1$ or $m1\mathbin {\}q>1$.
Keywords:
paper deals blow up properties solutions semilinear parabolic system weighted localized terms subject homogeneous dirichlet boundary conditions investigate influence three factors localized sources local sources t t weight functions asymptotic behavior solutions obtain uniform blow up profiles only cases leq mathbin amp mathbin amp
Affiliations des auteurs :
Haihua Lu
1
;
Feng Wang
2
;
Qiaoyun Jiang
3
1
Department of Mathematics Southeast University Nanjing 211189, P.R. China and Department of Mathematics Nantong University Nantong 226019, P.R. China
2
School of Mathematics and Physics Changzhou University Changzhou 213164, P.R. China
3
Department of Mathematics Nantong University Nantong 226019, P.R. China
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author = {Haihua Lu and Feng Wang and Qiaoyun Jiang},
title = {The analysis of blow-up solutions to a semilinear parabolic system with weighted localized terms},
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Haihua Lu; Feng Wang; Qiaoyun Jiang. The analysis of blow-up solutions to a semilinear parabolic system with weighted localized terms. Annales Polonici Mathematici, Tome 102 (2011) no. 2, pp. 187-203. doi: 10.4064/ap102-2-6
