Semilinear viscous Moore-Gibson-Thompson equation with the derivative-type nonlinearity: Global existence versus blow-up

Abstract

In this paper, we study global existence and blow-up of solutions to the viscous Moore-Gibson-Thompson (MGT) equation with the nonlinearity of derivative-type |ut|p. We demonstrate global existence of small data solutions if p>1+4/n (n≤6) or p≥2−2/n (n≥7), and blow-up of nontrivial weak solutions if 1<p≤1+1/n. Deeply, we provide estimates of solutions to the nonlinear problem. These results complete the recent works for semilinear MGT equations by [4].

Keywords

• moore-gibson-thompson equation
• derivative-type nonlinearity
• global existence of small data solution
• decay estimate
• blow-up