Global existence and blowup in infinite time for a fourth order wave equation with damping and logarithmic strain terms

Abstract

<p style='text-indent:20px;'>We consider the well-posedness of solution of the initial boundary value problem to the fourth order wave equation with the strong and weak damping terms, and the logarithmic strain term, which was introduced to describe many complex physical processes. The local solution is obtained with the help of the Galerkin method and the contraction mapping principle. The global solution and the blowup solution in infinite time under sub-critical initial energy are also established, and then these results are extended in parallel to the critical initial energy. Finally, the infinite time blowup of solution is proved at the arbitrary positive initial energy.</p>

Blow-up results for a Boussinesq-type plate equation with a logarithmic damping term and variable-exponent nonlinearities

“…This theorem could be proved by the Faedo-Galerkin approximation method. For details we refer the reader to [11,14,18,[21][22][23].…”

“…The main ingredient of their work is the introduction of several conditions on initial data leading to global existence of solutions with finite time blow-up. In another study, Pang et al [18] studied the global existence and blow-up in infinite time for the following fourth-order wave equation with damping and logarithmic strain terms:…”