Comptes Rendus
no. 9
Partial differential equations
Blow-up of solutions to a semilinear heat equation with a viscoelastic term and a nonlinear boundary flux
[Explosion de solutions de l'équation de la chaleur semi-linéaire avec un terme viscoélastique et un flux de limite non linéaire]

Présenté par : the Editorial Board

Yuzhu Han1 ; Wenjie Gao1 ; Haixia Li2
1 School of Mathematics, Jilin University, Changchun 130012, PR China
2 School of Mathematics, Changchun Normal University, Changchun 130032, PR China
Comptes Rendus. Mathématique, Volume 353 (2015) no. 9, pp. 825-830.

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

ut−Δu+∫0tg(t−s)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.

In this article, we study a semilinear heat equation

ut−Δu+∫0tg(t−s)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.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2015.07.003

Yuzhu Han 1 ; Wenjie Gao 1 ; Haixia Li 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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Yuzhu Han; Wenjie Gao; Haixia Li. 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. https://comptes-rendus.academie-sciences.fr/mathematique/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).

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