Blow-up of solutions for the Moore-Gibson-Thompson equations on exterior domain in two dimensions

Abstract

This paper is devoted to investigating blow-up of solutions to initial boundary value problem of the Moore-Gibson-Thompson (MGT) equations on exterior domain in two dimensions. More precisely, upper bound lifespan estimates of solutions to the problem with power nonlinearity $|u|^{p}$, derivative nonlinearity $|u_{t}|^{p}$ and combined nonlinearities $|u_{t}|^{p} + |u|^{q}$ in the sub-critical and critical cases are established, respectively. The proofs are based on the new test function technique. Our main new contribution is that we improve the results in [36] in two dimensions. It is worth to mention that lifespan estimates of solutions are associated with the well-known Strauss and Glassey conjecture. Moreover, the variation trend of wave for the Cauchy problem of linear MGT equation with different initial values in two dimensions is showed by numerical simulation.