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

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 $$\mathbb {R}^N\times (0,T)$$ R N × ( 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.