Pseudo almost periodic mild solutions to hyperbolic evolution equations in intermediate Banach spaces

Abstract

This article deals with the existence and uniqueness of pseudo almost periodic (mild) solutions to the class of partial evolution equations

where A is a sectorial operator on a Banach space , which is not necessarily densely defined and (hyperbolic), B is a linear operator on , and is pseudo almost periodic with being an abstract intermediate Banach space. Under some appropriate assumptions, we obtain the existence and uniqueness of such solutions in . An application to semilinear transport-like equations is given.

Keywords:

• Sectorial operator
• Analytic semigroup
• Hyperbolic semigroup
• Almost periodic
• Pseudo almost periodic
• Hyperbolic evolution equation

Keywords:

• 2000 Mathematics Subject Classifications:34G20
• 47A55

Notes

§When paper was first submitted author was visiting Department of Mathematical Sciences, University of Delaware, Newark, DE 19716, USA

Additional information

Notes on contributors

Gaston M. N'gué ré kata§

§When paper was first submitted author was visiting Department of Mathematical Sciences, University of Delaware, Newark, DE 19716, USA