On the Jordan-Moore-Gibson-Thompson wave equation in hereditary fluids with quadratic gradient nonlinearity

Abstract

We prove global solvability of the third-order in time Jordan-More-Gibson-Thompson acoustic wave equation with memory in ${\mathbb{R}}^n$, where $n\ge 3$. This wave equation models ultrasonic propagation in relaxing hereditary fluids and incorporates both local and cumulative nonlinear effects. The proof of global solvability is based on a sequence of high-order energy bounds that are uniform in time, and derived under the assumption of an exponentially decaying memory kernel and sufficiently small and regular initial data.

References in corpus (3)

• Moore-Gibson-Thompson equation with memory, part I: exponential decay of energy
• Optimal scalar products in the Standard Linear Viscoelastic Model
• Wellposedness and decay rates for the Cauchy problem of the Moore-Gibson-Thompson equation arising in high intensity ultrasound

Cited by in corpus (4)

• The Cauchy problem for the Moore-Gibson-Thompson equation in the dissipative case
• Asymptotic behaviors for the Jordan-Moore-Gibson-Thompson equation in the viscous case
• Asymptotic profiles and singular limits for the viscoelastic damped wave equation with memory of type I
• On the Cauchy problem for acoustic waves in hereditary fluids: decay properties and inviscid limits