Well‐posedness for the fourth‐order Moore–Gibson–Thompson equation in the class of Banach‐space‐valued Hölder‐continuous functions. (10th August 2022)

• Record Type: Journal Article
• Authors: Murillo‐Arcila, Marina
• Is Part Of: Mathematical methods in the applied sciences. Volume 46:Number 2(2023)
• Page Start: 1928
• Page End: 1937
• Publication Date: 2022-08-10
• Subjects: Cα$$ {C}^{\alpha } $$‐well posedness -- Dirichlet Laplacian -- Fourier multipliers -- fourth‐order Moore–Gibson–Thompson equation; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.8618
• Languages: English
• ISSNs: 0170-4214

Abstract

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 $$ {\dot{C}}^{\alpha } $$ ‐Fourier multipliers. We illustrate our results by providing an example based on the fourth order Moore–Gibson–Thompson equation with Dirichlet boundary conditions.