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Blow-up for semilinear parabolic equations with nonlinear memory

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Abstract

In this paper, we consider the semilinear parabolic equation \(u_t-\Delta u=u^q\int^{t}_{0}u^p(x,s)ds,\ \ \ x \in \Omega,\ \ t>0\) with homogeneous Dirichlet boundary conditions, where p, q are nonnegative constants. The blowup criteria and the blowup rate are obtained.

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Authors and Affiliations

  1. Department of Mathematics, Nanjing University, 210093, Nanjing, P.R. China

    Yuxiang Li

  2. Department of Mathematics, Nanjing University, 210093, Nanjing, P.R. China

    Chunhong Xie

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  1. Yuxiang Li
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  2. Chunhong Xie
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Correspondence to Yuxiang Li.

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Li, Y., Xie, C. Blow-up for semilinear parabolic equations with nonlinear memory . Z. angew. Math. Phys. 55, 15–27 (2004). https://doi.org/10.1007/s00033-003-1128-6

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  • DOI: https://doi.org/10.1007/s00033-003-1128-6

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