Electron. J. Differential Equations, Vol. 2019 (2019), No. 08, pp. 1-18.

p-biharmonic parabolic equations with logarithmic nonlinearity

Jiaojiao Wang, Changchun Liu

Abstract:
We consider an initial-boundary-value problem for a class of p-biharmonic parabolic equation with logarithmic nonlinearity in a bounded domain. We prove that if $2<p<q<p(1+\frac{4}{n})$ and $u_0\in W^+$, the problem has a global weak solutions; if $2<p<q<p(1+\frac{4}{n})$ and $u_0\in W_1^-$, the solutions blow up at finite time. We also obtain the results of blow-up, extinction and non-extinction of the solutions when $\max\{1,\frac{2n}{n+4}\}<p\leq2$.

Submitted July 26, 2018. Published January 22, 2019.
Math Subject Classifications: 35K35, 35A01, 35K55.
Key Words: p-biharmonic parabolic equation; blow-up; decay; extinction; non-extinction.

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Jiaojiao Wang
School of Mathematics
Jilin University
Changchun 130012, China
email: wjj16@mails.jlu.edu.cn
Changchun Liu
School of Mathematics
Jilin University
Changchun 130012, China
email: liucc@jlu.edu.cn

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