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Openness of the Set of Non-characteristic Points and Regularity of the Blow-up Curve for the 1 D Semilinear Wave Equation

✍ Scribed by Frank Merle; Hatem Zaag

Publisher
Springer
Year
2008
Tongue
English
Weight
478 KB
Volume
282
Category
Article
ISSN
0010-3616

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πŸ“œ SIMILAR VOLUMES

On the regularity of the blow-up set for
On the regularity of the blow-up set for semilinear heat equations
✍ Hatem Zaag πŸ“‚ Article πŸ“… 2002 πŸ› Elsevier Science 🌐 English βš– 293 KB

We consider u(x, t) a blow-up solution of u t = u + |u| p-1 u where u : R N Γ— [0, T ) β†’ R, p > 1, (N -2)p < N + 2 and either u(0) 0 or (3N -4)p < 3N + 8. The blow-up set S βŠ‚ 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

Asymptotic analysis and estimates of blo
Asymptotic analysis and estimates of blow-up time for the radial symmetric semilinear heat equation in the open-spectrum case
✍ N. I. Kavallaris; A. A. Lacey; C. V. Nikolopoulos; D. E. Tzanetis πŸ“‚ Article πŸ“… 2007 πŸ› John Wiley and Sons 🌐 English βš– 303 KB πŸ‘ 1 views

## Abstract We estimate the blow‐up time for the reaction diffusion equation __u__~__t__~=Ξ”__u__+ Ξ»__f__(__u__), for the radial symmetric case, where __f__ is a positive, increasing and convex function growing fast enough at infinity. Here Ξ»>Ξ»^\*^, where Ξ»^\*^ is the β€˜extremal’ (critical) value for