Finite-Time Blow-Up of Solutions to Semilinear Wave Equations
β Scribed by Eugene Belchev; Mariusz Kepka; Zhengfang Zhou
- Publisher
- Elsevier Science
- Year
- 2002
- Tongue
- English
- Weight
- 160 KB
- Volume
- 190
- Category
- Article
- ISSN
- 0022-1236
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π SIMILAR VOLUMES
0 with the Dirichlet, Neumann, or periodic boundary condition. Here ) 0 is a Ε½ . parameter, and f is an odd function of u satisfying f Π 0 ) 0 and some convexity Ε½ . w x condition. Let z U be the number of times of sign changes for U g C 0, 1 . It is Γ 4 shown that there exists an increasing sequenc
## 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, following the ideas of Lax, we prove a blow-up result for a class of solutions of the equation & -&x -&+xx -= 0, corresponding, in certain cases, to the development of a singularity in the second derivatives of 4. These solutions solve locally (in time) the Cauchy problem for smooth i
## Communicated by S. Chen The main purpose of this paper is concerned with blow-up smooth solutions to Navier-Stokes-Poisson (N-S-P) equations. First, we present a sufficient condition on the blow up of smooth solutions to the N-S-P system. Then we construct a family of analytical solutions that