A higher speed type II blow-up for the 4-d Fujita equation

Jianfeng Zhao

A higher speed type II blow-up for the 4-d Fujita equation

Analysis of PDEs 2022-09-26 v2

Authors: Jianfeng Zhao

Abstract

This paper is concerned with blow-up solutions of the 4-dimensional energy critical heat equation $u_t=\Delta u + u^3$ . Our main result is to show that the existence of type II blowup solutions, and $\|u(\cdot,t)\|_\infty\sim(T-t)^{-k}|ln(T-t)|^{\frac{2k}{2k-1}}, (k=1,2,3\cdots)$ .The inner-outer gluing method has been employed.

Keywords

fujita equation blow-up solutions type ii blowup energy critical heat equation inner-outer gluing method higher speed blow-up

Cite

@article{arxiv.2209.08580,
  title  = {A higher speed type II blow-up for the 4-d Fujita equation},
  author = {Jianfeng Zhao},
  journal= {arXiv preprint arXiv:2209.08580},
  year   = {2022}
}

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