Compact Almost Automorphic Solutions to Poisson’s and Heat Equations

Chávez A.; Khalil K.; Pereyra A.; Pinto M. · Bulletin of the Malaysian Mathematical Sciences Society (2024) · DOI: 10.1007/s40840-023-01637-5

Resumen

In the present work, we revisit several structural properties of almost automorphic and compact almost automorphic functions from the Euclidean space Rm (m≥ 1) with values in a Banach space X . When X is a Banach algebra, it is proven that the spaces formed by these functions are also Banach algebras. As applications, first we prove regularity of almost automorphic solution of Poisson’s equation; that is, we prove that bounded continuous functions with weak (distributional) almost automorphic Laplacian are compact almost automorphic; then, we prove the compact almost automorphy in space variable of classical solutions to heat equation with almost automorphic initial datum.

Instituciones: Universidad Nacional de Trujillo