Non-linear Time Degenerate Parabolic Inequalities and Applications
β Scribed by D.B. Dhaigude; D.Y. Kasture
- Publisher
- Elsevier Science
- Year
- 1993
- Tongue
- English
- Weight
- 184 KB
- Volume
- 175
- Category
- Article
- ISSN
- 0022-247X
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## 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
We give new finite time blow-up results for the non-linear parabolic equations u, -Au = up and u, -Au + pIVul4 = up. We first establish an a priori bound in Lpf ' for the positive non-decreasing global solutions. As a consequence, we prove in particular that for the second equation on RN, with q = 2