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Blow-up of solutions to a semilinear heat equation with a viscoelastic term and a nonlinear boundary flux

Resource Type: article
Authors: Han, Yuzhu; Gao, Wenjie; Li, Haixia
Source: Comptes Rendus. Mathématique, Vol 353, Iss 9, Pp 825-830 (2015)
Subject: Mathematics
QA1-939
Language: English
French
ISSN: 1778-3569

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In this article, we study a semilinear heat equation \[ {u}_{t}-\mathrm{\Delta }u+\underset{0}{\overset{t}{\int }}g(t-s)\mathrm{\Delta }u(x,s)\phantom{\rule{0.25em}{0ex}}\mathrm{d}s=0 \] with a viscoelastic term and a nonlinear flux on the boundary. By defining a modified energy functional and using a concavity argument, a blow-up result for solutions with negative initial energy is proved.

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Blow-up of solutions to a semilinear heat equation with a viscoelastic term and a nonlinear boundary flux

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