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Null and approximate controllability for weakly blowing up semilinear heat equations

✍ Scribed by Enrique Fernández-Cara; Enrique Zuazua

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
209 KB
Volume
17
Category
Article
ISSN
0294-1449

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On the regularity of the blow-up set for
On the regularity of the blow-up set for semilinear heat equations
✍ Hatem Zaag 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 293 KB

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