Non-linear partial differential equations with discrete state-dependent delays in a metric space

TL;DR

This paper studies a class of non-linear PDEs with discrete state-dependent delays, establishing existence, uniqueness, and long-term behavior of solutions within a specialized metric space.

Contribution

It introduces a framework for analyzing non-linear PDEs with state-dependent delays, proving well-posedness and the existence of a global attractor.

Findings

Existence and uniqueness of strong solutions

Construction of a dynamical system in a metric space

Proof of a compact global attractor

Abstract

We investigate a class of non-linear partial differential equations with discrete state-dependent delays. The existence and uniqueness of strong solutions for initial functions from a Banach space are proved. To get the well-posed initial value problem we restrict our study to a smaller metric space, construct the dynamical system and prove the existence of a compact global attractor.