Construction of blow-up solution for 5 dimentional critical fujita type equation with different blow-up speed

2020/08/10 by Liqun Zhang, Zhang, Liqun, Jianfeng Zhao +1
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #Differential Equations and Numerical Methods #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2008.03890

openalex publication_date 2020/08/10 · openalex created_date 2020/08/13 · openalex updated_date 2026/07/28

Abstract

We are concerned with blow-up solutions of the 5-dimensional energy critical heat equation u_t=Δu + | u |^(4)/(3)u. Our main result is to show that the existence of type 2 solutions blows up at 2 points with 2 different blow-up rates. The inner-outer gluing method has been employed.

Citations

• Singularity formation for the two-dimensional harmonic map flow into S²
• Geometry driven Type II higher dimensional blow-up for the critical heat equation
• A type II blowup for the six dimensional energy critical heat equation

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