In this paper we study the critical exponents of the Cauchy problem in R n of the quasilinear singular parabolic equations: u t = div โu m-1 โu + t s x ฯ u p , with non-negative initial data. Here s โฅ 0 n -1 / n + 1 < m < 1 p > 1 and ฯ > n 1 -m -1 + m + 2s . We prove that p c โก m + 1 + m + 2s + ฯ /n
โฆ LIBER โฆ
Quasilinear Riccati Type Equations with Super-Critical Exponents
โ Scribed by Phuc, Nguyen Cong
- Book ID
- 120940313
- Publisher
- Taylor and Francis Group
- Year
- 2010
- Tongue
- English
- Weight
- 216 KB
- Volume
- 35
- Category
- Article
- ISSN
- 0360-5302
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## Abstract We study the Cauchy problem for the quasilinear parabolic equation magnified image where __p__ > 1 is a parameter and ฯ is a smooth, bounded function on (1, โ) with โ โฉฝ __s__ฯโฒ(__s__)/ฯ(__s__) โฉฝ ฮธ for some ฮธ > 0. If 1 < __p__ < 1 + 2/__N__, there are no global positive solutions, wherea
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