On Some Nonlocal in Time and Space Parabolic Problem

TL;DR

This paper investigates nonlinear parabolic problems that are nonlocal in both time and space, establishing existence, uniqueness, and asymptotic behavior of solutions.

Contribution

It introduces new results on the existence, uniqueness, and long-term behavior of solutions for nonlocal nonlinear parabolic problems.

Findings

Proved existence of solutions under certain conditions

Established uniqueness in specific cases

Analyzed the asymptotic behavior of solutions

Abstract

The goal of this note is to study nonlinear parabolic problems nonlocal in time and space. We first establish the existence of a solution and its uniqueness in certain cases. Finally we consider its asymptotic behaviour.