Existence of Weighted Pseudo Almost Periodic Solutions to Some Classes of Nonautonomous Partial Evolution Equations

TL;DR

This paper establishes the existence of weighted pseudo almost periodic solutions for certain nonautonomous partial evolution equations using advanced mathematical techniques, with applications to heat equations with gradient coefficients.

Contribution

It introduces new existence results for weighted pseudo almost periodic solutions under Acquistpace-Terreni conditions for nonautonomous PDEs.

Findings

Existence of solutions under specific conditions

Application to nonautonomous heat equations

Use of interpolation spaces and exponential dichotomy techniques

Abstract

In this paper, under Acquistpace-Terreni conditions, we make extensive use of interpolation spaces and exponential dichotomy techniques to obtain the existence of weighted pseudo almost periodic solutions to some classes of nonautonomous partial evolution equations. Applications include the existence of weighted pseudo almost periodic solutions to a nonautonomous heat equation with gradient coefficients.