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

Abstract

This paper is devoted to studying a nonlocal parabolic equation with logarithmic nonlinearity ulog|u|−⨏Ωulog|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.