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On the blow-up rate and the blow-up set of breaking waves for a shallow water equation

✍ Scribed by Adrian Constantin; Joachim Escher

Publisher: Springer-Verlag
Year: 2000
Tongue: French
Weight: 132 KB
Volume: 233
Category: Article
ISSN: 0025-5874
DOI: 10.1007/pl00004793

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We consider u(x, t) a blow-up solution of u t = u + |u| p-1 u where u : R N × [0, T ) → R, p > 1, (N -2)p < N + 2 and either u(0) 0 or (3N -4)p < 3N + 8. The blow-up set S ⊂ 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