Infinite time blow-up of solutions for a plate equation with weak damping and logarithmic nonlinearity

Abstract

This paper considers a plate equation with weak damping and logarithmic nonlinearity, which can be used to model the deformations and internal forces of an elastic plate under external factors such as lateral loads. We prove the solution blows up at infinity with subcritical and critical initial energies. Moreover, we establish the infinite time blow-up result at arbitrarily high initial energy. These results complement earlier results in the literature.