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Blow-up set for type I blowing up solutions for a semilinear heat equation

โœ Scribed by Fujishima, Yohei; Ishige, Kazuhiro


Book ID
121377915
Publisher
Elsevier Science
Year
2014
Tongue
English
Weight
723 KB
Volume
31
Category
Article
ISSN
0294-1449

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On the regularity of the blow-up set for
โœ Hatem Zaag ๐Ÿ“‚ Article ๐Ÿ“… 2002 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 293 KB

We consider u(x, t) a blow-up solution of u t = u + |u| p-1 u where u : R N ร— [0, T ) โ†’ R, p > 1, (N -2)p < N + 2 and either u(0) 0 or (3N -4)p < 3N + 8. The blow-up set S โŠ‚ R N of u is the set of all blow-up points. Under a nondegeneracy condition, we show that if S is continuous, then it is a C 1