Well-posedness for the fourth-order Moore-Gibson-Thompson equation in Hölder Continuous Function Spaces

Abstract

In this work, we provide a full characterization of well-posedness in vector-valued Hölder continuous function spaces for a fourth-order abstract evolution equation arising from the Moore–Gibson–Thompson equation with memory using operator-valued (Formula presented.) -Fourier multipliers. We illustrate our results by providing an example based on the fourth order Moore–Gibson–Thompson equation with Dirichlet boundary conditions.