Asymptotic behavior for a singular diffusion equation with gradient absorption

TL;DR

This paper investigates the long-term behavior of solutions to a nonlinear diffusion equation with gradient absorption, revealing asymptotic properties and decay rates for large times.

Contribution

It provides new insights into the asymptotic behavior of solutions to a singular diffusion equation with gradient absorption, extending previous results.

Findings

Characterization of the asymptotic profile of solutions

Derivation of decay rates for large time

Identification of conditions for solution convergence

Abstract

We study the large time behavior of non-negative solutions to the singular diffusion equation with gradient absorption $$ \partial_t u-\Delta_{p}u+|\nabla u|^q=0 \quad \hbox{in} \ (0,\infty)\times\real^N, $$ for $p_c:=2N/(N+1)