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

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.