Blow‐up and lifespan estimates of solutions to the weakly coupled system of semilinear Moore–Gibson–Thompson equations

Abstract

This work is devoted to investigating formation of singularities of solutions to the weakly coupled system of semilinear Moore–Gibson–Thompson equations with power nonlinearities |v|p, |u|q, derivative nonlinearities |vt|p, |ut|q, mixed nonlinearities |v|q, |ut|p, and combined nonlinearities , respectively. Upper bound lifespan estimates of solutions to the problem in the subcritical and critical cases are also established. The main tool employed in the proofs is test function technique. The novelty is that lifespan estimates of solutions are connected with the well‐known Strauss exponent and Glassey exponent.