The analysis of blow-up solutions to a semilinear parabolic system with weighted localized terms

Volume 102 / 2011

Haihua Lu, Feng Wang, Qiaoyun Jiang Annales Polonici Mathematici 102 (2011), 187-203 MSC: 35K15, 35K65. DOI: 10.4064/ap102-2-6

Abstract

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 $m>1 \mathbin {\&}q<1$ or $m<1\mathbin {\&}q>1$.

Authors

  • Haihua LuDepartment of Mathematics
    Southeast University
    Nanjing 211189, P.R. China
    and
    Department of Mathematics
    Nantong University
    Nantong 226019, P.R. China
    e-mail
  • Feng WangSchool of Mathematics and Physics
    Changzhou University
    Changzhou 213164, P.R. China
    e-mail
  • Qiaoyun JiangDepartment of Mathematics
    Nantong University
    Nantong 226019, P.R. China
    e-mail

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