High Energy Blowup for a Class of Wave Equations With Critical Exponential Nonlinearity

Abstract

The goal of this paper is to investigate the finite-time blow-up of weak solutions to a class of wave equations involving the fractional 1/2 -Laplace operator with critical exponential growth, where the initial energy is supercritical. These results extend the recent work regarding the finite-time blow-up of weak solutions. We emphasize that there are no effective methods to study this problem. Hence, we need to find some suitable assumptions and the appropriate technique to achieve this.