Initial-Boundary Value Problems for Parabolic Equations

TL;DR

This paper establishes new existence and uniqueness results for weak solutions to non-homogeneous initial-boundary value problems involving parabolic equations related to the p-Laplacian.

Contribution

It provides novel theoretical results on the solvability of parabolic equations with non-homogeneous boundary conditions involving the p-Laplacian.

Findings

Proved existence of weak solutions.

Proved uniqueness of weak solutions.

Extended results to non-homogeneous boundary conditions.

Abstract

We prove new existence and uniqueness results for weak solutions to non-homogeneous initial-boundary value problems for parabolic equations modeled on the evolution of the p-Laplacian.