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 false|vtfalse|p1+false|vfalse|q1,0.1emfalse|utfalse|p2+false|ufalse|q2, 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.

Formation of singularities of solutions to the Cauchy problem for semilinear Moore-Gibson-Thompson equations

“…Scholars are devoted to investigating blow-up of solution to the Cauchy problem (1.1) with nonlinear terms f (u, u t ) = |u| p , |u t | p , |u t | p +|u| q (see [2,5,6,21,25,26]). Firstly, we recall physical backgrounds of the linear MGT equation τ u ttt + u tt − c 2 ∆u − b∆u t = 0.…”

“…It is worth to point out that Ming et al[21] illustrate lifespan estimates of solutions to problem (1.2) with |v t | p1 +|v| q1 , |u t | p2 +|u| q2 in the sub-critical case. We derive lifespan estimates of solutions in the critical case (see Theorem 1.4).…”