The existence, general decay and blow-up for a plate equation with nonlinear damping and a logarithmic source term

Abstract

<p style="text-indent:20px;">In this paper, we consider a plate equation with nonlinear damping and logarithmic source term. By the contraction mapping principle, we establish the local existence. The global existence and decay estimate of the solution at subcritical initial energy are obtained. We also prove that the solution with negative initial energy blows up in finite time under suitable conditions. Moreover, we also give the blow-up in finite time of solution at the arbitrarily high initial energy for linear damping (i.e. <inline-formula><tex-math id="M1">$ m = 2 $</tex-math></inline-formula>).</p>