Partial differential equations
Blow-up of solutions to a semilinear heat equation with a viscoelastic term and a nonlinear boundary flux
Comptes Rendus. Mathématique, Volume 353 (2015) no. 9, pp. 825-830.

In this article, we study a semilinear heat equation

utΔu+0tg(ts)Δu(x,s)ds=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.

Dans cet article, on étudie une équation de la chaleur semi-linéaire

utΔu+0tg(ts)Δu(x,s)ds=0
avec un terme viscoélastique et un flux non linéaire sur la limite. En définissant une modifiée fonctionnelle d'énergie et en utilisant un argument de concavité, un résultat d'explosion des solutions avec énergie initiale négative est prouvé.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2015.07.003
Han, Yuzhu 1; Gao, Wenjie 1; Li, Haixia 2

1 School of Mathematics, Jilin University, Changchun 130012, PR China
2 School of Mathematics, Changchun Normal University, Changchun 130032, PR China
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Han, Yuzhu; Gao, Wenjie; Li, Haixia. Blow-up of solutions to a semilinear heat equation with a viscoelastic term and a nonlinear boundary flux. Comptes Rendus. Mathématique, Volume 353 (2015) no. 9, pp. 825-830. doi : 10.1016/j.crma.2015.07.003. http://www.numdam.org/articles/10.1016/j.crma.2015.07.003/

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The project is supported by NSFC (11271154, 11401252), by Science and Technology Development Project of Jilin Province (20150201058NY) and by the 985 program of Jilin University. The first author is also supported by Fundamental Research Funds of Jilin University (450060501179).