Moore–Gibson–Thompson equation with memory, part I: exponential decay of energy


We are interested in the Moore–Gibson–Thompson equation with memory(Formula presented.).This model arises in high-frequency ultrasound applications accounting for thermal flux and molecular relaxation times. According to revisited extended irreversible thermodynamics, thermal flux relaxation leads to the third-order derivative in time while molecular relaxation leads to non-local effects governed by memory terms. The resulting model is of hyperbolic type with viscous effects. We first classify the memory into three types. Then, we study how a memory term creates damping mechanism and how the memory causes energy decay even in the cases when the original memoryless system is unstable.

Publication Title

Zeitschrift fur Angewandte Mathematik und Physik