Geodesic
A higher speed type II blowup for the five dimensional energy critical heat equation
Annales de l'I.H.P. Analyse non linéaire, Tome 37 (2020) no. 2, pp. 309-341

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This paper is concerned with blow-up solutions of the five dimensional energy critical heat equation ut=Δu+|u|43u. A goal of this paper is to show the existence of type II blowup solutions which behave as ‖u(t)‖∞∼(T−t)−3k (k=2,3,⋯). These solutions are the same ones formally derived by Filippas, Herrero and Velázquez [8]. We find a mistake in their blowup rate and correct it.

DOI : 10.1016/j.anihpc.2019.09.006
Keywords: Semilinear heat equation, Energy critical, Type II blowup, Matched asymptotic expansion 
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     author = {Harada, Junichi},
     title = {A higher speed type {II} blowup for the five dimensional energy critical heat equation},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {309--341},
     publisher = {Elsevier},
     volume = {37},
     number = {2},
     year = {2020},
     doi = {10.1016/j.anihpc.2019.09.006},
     mrnumber = {4072807},
     zbl = {1433.35007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2019.09.006/}
}
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Harada, Junichi. A higher speed type II blowup for the five dimensional energy critical heat equation. Annales de l'I.H.P. Analyse non linéaire, Tome 37 (2020) no. 2, pp. 309-341. doi: 10.1016/j.anihpc.2019.09.006

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