Singular solutions of some nonlinear parabolic equations with spatially inhomogeneous absorption

TL;DR

This paper investigates the asymptotic behavior of solutions to certain nonlinear parabolic equations with spatially varying strong absorption, identifying conditions leading to pointwise singularities or persistent razor blade singularities.

Contribution

It provides a detailed analysis of the limit behavior and singularity formation in nonlinear parabolic equations with inhomogeneous absorption, highlighting two distinct phenomena.

Findings

Identification of conditions for pointwise singularities.

Discovery of persistent razor blade singularities.

Characterization of solution behavior near singularities.

Abstract

We study the limit behaviour of solutions of a class of solutions of nonlinear parabolic equations with a degenerate strong absorption. We prove that two types of phenomena can occur: the pointwise singularity or the formation of razor blades (or persistent singularities).