Trudinger's Parabolic Equation

TL;DR

This paper investigates the uniqueness of non-negative solutions to a nonlinear parabolic PDE involving the p-Laplacian, using basic estimates derived via the Galerkin Method.

Contribution

It establishes uniqueness results for solutions of a nonlinear parabolic equation with a focus on the p-Laplacian operator.

Findings

Derived basic estimates for solutions.

Proved uniqueness of non-negative solutions.

Applied Galerkin Method for analysis.

Abstract

We study the uniqueness of non-negative solutions of the equation \begin{align*} \partial_t\left(|u|^{p-2}u\right)\,=\, \operatorname{div}(|\nabla u|^{p-2}\nabla u). \end{align*} Basic estimates are derived with the Galerkin Method.