Stability of nondegenerate ODE type blowup for the Fujita type heat equation

TL;DR

This paper investigates the stability of nondegenerate ODE type blowup solutions for the Fujita type heat equation, extending previous results to more general cases and analyzing their asymptotic behavior.

Contribution

It generalizes the stability results of nondegenerate ODE type blowup solutions for the Fujita heat equation beyond the previously known parameter range.

Findings

Stability of nondegenerate ODE type blowup solutions confirmed in broader settings.

Extension of stability results to more general cases.

Analysis of asymptotic behavior of blowup solutions.

Abstract

The asymptotic bahavior of blowup solutions to the Fujita type heat equation $u_t=\Delta u+|u|^{p-1}u$ is studied. This equation admits the ODE type blowup given by $u(x,t)=(p-1)^\frac{1}{p-1}(T-t)^{-\frac{1}{p-1}}$. It is known that nondegenerate ODE type blowup is stable if $p\in(1,\frac{n+2}{n-2})$ due to Fermanian Kammerer-Merle-Zaag (2000). This paper extends their result to more general case.