Bubble towers in the ancient solution of energy-critical heat equation

TL;DR

This paper constructs a special ancient solution to the energy-critical heat equation in high dimensions, exhibiting blow-up behavior with multiple bubble profiles as time goes backward.

Contribution

It introduces a new radially smooth ancient solution with multiple Talenti bubbles for the energy-critical heat equation in dimensions n ≥ 7.

Findings

Constructed a radially smooth positive ancient solution

Solution exhibits blow-up at the origin with bubble profiles

Applicable for dimensions n ≥ 7

Abstract

We construct a radially smooth positive ancient solution for energy critical semi-linear heat equation in $\mathbb{R}^n$, $n\geq 7$. It blows up at the origin with the profile of multiple Talenti bubbles in the backward time infinity.