On backward self-similar blow-up solutions to a supercritical semilinear heat equation
2010 ◽
Vol 140
(4)
◽
pp. 821-831
◽
Keyword(s):
Blow Up
◽
We are concerned with a Cauchy problem for the semilinear heat equationthen u is called a backward self-similar solution blowing up at t = T. Let pS and pL be the Sobolev and the Lepin exponents, respectively. It was shown by Mizoguchi (J. Funct. Analysis257 (2009), 2911–2937) that k ≡ (p − 1)−1/(p−1) is a unique regular radial solution of (P) if p > pL. We prove that it remains valid for p = pL. We also show the uniqueness of singular radial solution of (P) for p > pS. These imply that the structure of radial backward self-similar blow-up solutions is quite simple for p ≥ pL.
1990 ◽
Vol 115
(1-2)
◽
pp. 19-24
◽
1998 ◽
Vol 128
(4)
◽
pp. 745-758
◽
1999 ◽
Vol 129
(6)
◽
pp. 1197-1227
◽
2009 ◽
Vol 139
(5)
◽
pp. 897-926
◽