Existence, comparison principle and uniqueness for doubly nonlinear anisotropic evolution equation

TL;DR

This paper establishes existence, comparison principles, and uniqueness results for solutions to a class of doubly nonlinear anisotropic evolution equations, advancing the mathematical understanding of such complex PDEs.

Contribution

It introduces new existence and uniqueness results for doubly nonlinear anisotropic evolution equations under specific conditions.

Findings

Existence of solutions for Cauchy-Dirichlet problem.

Existence of solutions for the Cauchy problem on ^N(0,T).

Comparison principle and uniqueness results.

Abstract

We prove the existence of solutions to the Cauchy-Dirichlet problem associated with a class of doubly nonlinear anisotropic evolution equations. We also demonstrate the existence of solutions to the corresponding Cauchy problem on $\mathbb{R}^N\times(0,T)$. Under some assumptions on the Caratheodory vector field we prove a comparison principle and utilize it to obtain a uniqueness result for the Cauchy-Dirichlet problem.