Pseudo-Almost Automorphic ๐0-Solutions: Well-Posedness and Asymptotic Behaviour in Evolution Equations with Nonlocal Constraints
Abstract
This research establishes an innovative analytical framework for examining C0-solutions of pseudo-almost automorphic type in evolution systems governed by nonlocal initial conditions within Banach spaces. Our methodological approach is founded upon the compactness properties of the resolvent operator (IโA)โ1 and the semigroup generated by A. By integrating semigroup theory with fixed-point methodologies, we develop a unified strategy that successfully overcomes challenges arising from nonlocal initial specifications. The practical applicability of our theoretical framework is verified through its implementation on a transport equation with nonlocal initial history, thereby demonstrating both the existence of solutions and their distinctive character.
Fields of Study & Subjects
Nonlinear Differential Equations Analysis
Nonlinear Partial Differential Equations
Fixed Point Theorems Analysis
Publication details
- Journal / source
- Mathematics
- Publisher
- MDPI AG
- Volume
- 14
- Issue
- 3
- Pages
- 459โ459
- Publication date
- 28 January 2026
- Language
- EN