Blow-up and non-extinction for a nonlocal parabolic equation with logarithmic nonlinearity

Boundary Value Problems

Lijun Yan¹  Zuodong Yang² 

[1] Institute of Mathematics, School of Mathematics Science, Nanjing Normal University;School of Teacher Education, Nanjing Normal University;

关键词: Blow-up;    Non-extinction;    Nonlocal parabolic equation;   

DOI  :  10.1186/s13661-018-1042-7

来源: DOAJ

【 摘 要 】

Abstract This paper is devoted to studying a nonlocal parabolic equation with logarithmic nonlinearity ulog|u|−⨏Ωulog|u|dx $u\log |u|-\fint_{\Omega } u\log |u|\,dx$ in a bounded domain, subject to homogeneous Neumann boundary value condition. By using the logarithmic Sobolev inequality and energy estimate methods, we get the results under appropriate conditions on blow-up and non-extinction of the solutions, which extend some recent results.

【 授权许可】

Unknown