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 β 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
On the problem of preventing blowing-up and quenching for semilinear heat equation
β Scribed by Yan Zi-qian
- Publisher
- Springer
- Year
- 1986
- Tongue
- English
- Weight
- 276 KB
- Volume
- 7
- Category
- Article
- ISSN
- 0253-4827
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## Abstract Theoretical aspects related to the approximation of the semilinear parabolic equation: $u\_t=\Delta u+f(u)$\nopagenumbers\end, with a finite unknown βblowβupβ time __T__~b~ have been studied in a previous work. Specifically, for __Ξ΅__ a small positive number, we have considered coupled
This paper studies the problem ¨s d¨q ¨q y 1 y cos x ¨p , for 0x -1 and t ) 0, Ž . for x s 0, 1 and t ) 0, x ¨x, 0 s ¨x , for 0x -1, ## Ž . Ž . 0 where 1qp, d ) 0. It is shown that for large initial data if p -2 q y 1 or p s 2q y 1 but d is small, then the positive solution blows up in finite t