Blow-up solutions and global solutions for nonlinear parabolic problems
โ Scribed by Hailiang Zhang
- Publisher
- Elsevier Science
- Year
- 2008
- Tongue
- English
- Weight
- 409 KB
- Volume
- 69
- Category
- Article
- ISSN
- 0362-546X
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๐ SIMILAR VOLUMES
## Abstract In this paper the degenerate parabolic system __u__~__t__~=__u__(__u__~__xx__~+__av__). __vt__=__v__(__v__~__xx__~+__bu__) with Dirichlet boundary condition is studied. For $a. b {<} \lambda\_{1} (\sqrt {ab} {<} \lambda\_{1} {\rm if}\, \alpha\_{1} {\neq} \alpha\_{2})$, the global existe
When b s 0, Eq. 1.1 becomes usual semilinear wave equations. When ลฝ . b)0, we call Eq. 1.1 wave equations of Kirchhoff type which have been introduced in order to study the nonlinear vibrations of an elastic string by
We consider the blow-up of solutions of equations of the form by means of a differential inequality technique. A lower bound for blow-up time is determined if blow-up does occur as well as a criterion for blow-up and conditions which ensure that blow-up cannot occur.