Abstract
We are concerned with the blow-up solutions of the 5-dimensional energy critical heat equation \(u_t=\Delta u + | u |^{\frac{4}{3}}u\). Our main finding is to show that the existence of type II solutions results in blowing up at any k points, with arbitrary k blow-up rates. We have employed the inner–outer gluing method to accomplish this.
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This article was funded by Liqun Zhang (Grant no. 11471320).
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JZ wrote the main manuscript text, and LZ gives the idea and the computation of the outer problem. All authors reviewed the manuscript.
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Zhang, L., Zhao, J. Construction of blow-up solution for 5-dimensional critical Fujita-type equation with different blow-up speed. J. Fixed Point Theory Appl. 25, 67 (2023). https://doi.org/10.1007/s11784-023-01068-6
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DOI: https://doi.org/10.1007/s11784-023-01068-6