Regularity of viscous solutions for a degenerate nonlinear Cauchy problem

TL;DR

This paper investigates the regularity of solutions to a class of nonlinear degenerate parabolic equations using the vanishing viscosity method to establish generalized solutions.

Contribution

It introduces a new approach to analyze the regularity of solutions for degenerate nonlinear parabolic equations via the vanishing viscosity method.

Findings

Established regularity results for generalized solutions

Proved existence of solutions using vanishing viscosity

Provided insights into the behavior of degenerate parabolic equations

Abstract

We consider the Cauchy problem for a class of nonlinear degenerate parabolic equa- tion with forcing. By using the vanishing viscosity method we obtain generalized solutions. We prove some regularity results about this generalized solutions.