Dirichlet boundary conditions for degenerate and singular nonlinear parabolic equations

TL;DR

This paper establishes the existence and uniqueness of solutions to nonlinear degenerate parabolic equations with Dirichlet boundary conditions in bounded domains, using barrier functions to handle inhomogeneous conditions.

Contribution

It introduces a method to prove existence and uniqueness for a class of nonlinear degenerate parabolic equations with inhomogeneous Dirichlet boundary conditions.

Findings

Existence of solutions under specified conditions

Uniqueness of solutions for the class of equations

Use of barrier functions to handle boundary conditions

Abstract

We study existence and uniqueness of solutions to a class of nonlinear degenerate parabolic equations, in bounded domains. We show that there exists a unique solution which satisfies possibly inhomogeneous Dirichlet boundary conditions. To this purpose some barrier functions are properly introduced and used.