Asymptotic stability of singular solution to nonlinear heat equation

TL;DR

This paper investigates the long-term behavior of singular steady states in nonlinear heat equations, focusing on their stability in weighted Lebesgue spaces, which is crucial for understanding solution dynamics.

Contribution

It provides new insights into the asymptotic stability of singular solutions within weighted Lebesgue norms, extending previous stability analyses.

Findings

Singular steady states are asymptotically stable under certain conditions.

Weighted Lebesgue norms effectively characterize the stability behavior.

Results contribute to the understanding of solution dynamics in nonlinear heat equations.

Abstract

In this paper, we discuss the asymptotic stability of singular steady states of the nonlinear heat equation in the weighted Lebesgue norms.