Blow-up of solutions to a viscoelastic parabolic equation with positive initial energy

Boundary value problems

Haixia Li¹  Yuzhu Han² 

[1] School of Mathematics, Changchun Normal University, Changchun, P.R. China;School of Mathematics, Jilin University, Changchun, P.R. China

关键词: viscoelastic;    potential well method;    blow-up;    nonlinear boundary flux;   

DOI  :  10.1186/s13661-017-0821-x

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, a semilinear viscoelastic parabolic equation with nonlinear boundary flux is studied. Due to the comparison principle being invalid, potential well method and concavity argument are used to prove that the solutions blow up in finite time with positive initial energy. This result improves the one obtained by Han et al. (C. R. Math. Acad. Sci. Paris, Sér. I 353:825-830, 2015).

【 授权许可】

CC BY