Global existence and blow-up for a thermoelastic system with p-Laplacian

Abstract

In this paper, we study the following thermoelastic system with p-Laplacian $\begin{array}{r}\{\begin{array}{l}{\displaystyle u_{tt}-{\mathrm{\Delta }}_{p}u+\theta =|u{|}^{r-1}u,}\\ {\displaystyle {\theta }_t-\mathrm{\Delta }\theta =u_t}\end{array}\end{array}$in a bounded domain $\mathrm{\Omega }\subset {\mathbb{R}}^n$, where u and θ denote the elongation of a plate and the temperature difference to the equilibrium state, respectively; ${\mathrm{\Delta }}_p$ denotes the classical p-Laplacian operator. By employing the potential well theory, we discuss the properties of global existence and finite time blow-up for the solutions. Moreover, we give the lower and upper bounds of blow-up time to the blow-up solutions.

Keywords:

• Thermoelastic system
• p-Laplacian
• global existence
• blow-up
• blow-up time

2010 MSC:

• 35B40
• 93D20
• 74F05

Disclosure statement

No potential conflict of interest was reported by the author(s).