p-biharmonic parabolic equations with logarithmic nonlinearity

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 + 4/n) and u0 ∈ W+, the problem has a global weak solutions; if 2 < p < q < p(1 + 4/n) and u0 ∈ 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, 2n/n+4} < p ≤ 2.