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

Abstract

We are concerned with blow-up solutions of the 5-dimensional energy critical heat equation $u_t=\Delta u+|u{|}^{\frac{4}{3}}u$. 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.

References in corpus (4)

• Singularity formation for the two-dimensional harmonic map flow into $S^2$
• Geometry driven Type II higher dimensional blow-up for the critical heat equation
• Type II Finite time blow-up for the three dimensional energy critical heat equation
• A type II blowup for the six dimensional energy critical heat equation