Local Behavior near Blow-up Points for Semilinear Parabolic Equations
β Scribed by J.J.L. Velazquez
- Publisher
- Elsevier Science
- Year
- 1993
- Tongue
- English
- Weight
- 787 KB
- Volume
- 106
- Category
- Article
- ISSN
- 0022-0396
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π SIMILAR VOLUMES
## Communicated by H. A. Levine Consider the problem
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
We study a nonlinear parabolic equation with a superlinear reaction term. By studying the backward self-similar solutions for this equation, we construct a ΓΏnite number of self-similar single-point blow-up patterns with di erent oscillations.
## 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
In this paper, we study the following semilinear integro-di!erential equation of the parabolic type that arise in the theory of nuclear reactor kinetics: under homogeneous Dirichlet boundary condition, where p, q\*1. We "rst establish the local solvability of a large class of semilinear non-local e