Uniqueness, regularity and behaviour in time of the solutions to nonlinear anisotropic parabolic equations

TL;DR

This paper investigates the existence, uniqueness, and temporal behavior of solutions to nonlinear anisotropic parabolic equations, emphasizing the effects of initial data and forcing terms, with special focus on autonomous cases.

Contribution

It provides new results on the existence, uniqueness, and long-term behavior of solutions to a class of nonlinear anisotropic parabolic equations.

Findings

Existence and uniqueness of solutions established.

Behavior in time analyzed, especially for autonomous forcing terms.

Insights into the influence of initial data and forcing on solution dynamics.

Abstract

In this paper we study a class of nonlinear anisotropic parabolic problems in bounded domains. In detail, we study the influences of the initial data and the forcing term f on the behavior of the solutions. We prove existence and uniqueness results. We indagate on the behavior in time of the solutions with a particular attention to the autonomous case f(x, t) = f(x).