A Nonlinear Singular Diffusion Equation with Source

TL;DR

This paper investigates a nonlinear singular diffusion equation with source, establishing the existence, uniqueness, and continuous dependence of global smooth solutions on initial data, thus advancing understanding of such complex PDEs.

Contribution

It proves the existence and uniqueness of global smooth solutions for a nonlinear singular diffusion equation with boundary conditions, highlighting their dependence on initial data.

Findings

Existence of a unique global smooth solution

Continuous dependence on initial data

Advancement in understanding nonlinear singular diffusion equations

Abstract

In this paper, the existence, uniqueness and dependence on initial value of solution for a singular diffusion equation with nonlinear boundary condition are discussed. It is proved that there exists a unique global smooth solution which depends on initial data continuously.