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

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

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