Large solutions for nonlinear parabolic equations without absorption terms

TL;DR

This paper introduces a new concept of entropy solutions for nonlinear parabolic p-Laplacian equations with boundary blow-up, establishing their existence and uniqueness for various initial data conditions.

Contribution

It defines a suitable entropy solution framework for p-Laplacian equations with boundary blow-up and proves their existence and uniqueness.

Findings

Existence of entropy solutions for 1<p<2 and p=1 cases.

Uniqueness of these solutions under specified conditions.

Extension of solutions to boundary blow-up scenarios.

Abstract

In this paper we give a suitable notion of entropy solution of parabolic $p-$laplacian type equations with $1\leq p<2$ which blows up at the boundary of the domain. We prove existence and uniqueness of this type of solutions when the initial data is locally integrable (for $1<p<2$) or integrable (for $p=1$; i.e the Total Variation Flow case).