Well‐posedness for the fourth‐order Moore–Gibson–Thompson equation in the class of Banach‐space‐valued Hölder‐continuous functions. (10th August 2022) - Murillo‐Arcila, Marina
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 Ċ α $$ {\dot{C}}^{α } $$ ‐Fourier multipliers. We illustrate our results by providing an example based on the fourth order Moore–Gibson–Thompson equation with Dirichlet boundary conditions.