Construction of a stable blow-up solution for a class of strongly perturbed semilinear heat equations

TL;DR

This paper constructs a finite-time blow-up solution with a specific profile for a class of strongly perturbed semilinear heat equations, using reduction to finite dimensions and index theory.

Contribution

It introduces a novel method to construct blow-up solutions for perturbed heat equations with prescribed profiles, advancing understanding of singularity formation.

Findings

Successfully constructs blow-up solutions with prescribed profiles

Reduces the problem to a finite-dimensional analysis

Employs index theory to establish existence

Abstract

We construct a solution for a class of strongly perturbed semilinear heat equations which blows up in finite time with a prescribed blow-up profile. The construction relies on the reduction of the problem to a finite dimensional one and the use of index theory to conclude.