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The critical exponent of degenerate parabolic systems

โœ Scribed by Yuan-Wei Qi; H. A. Levine


Publisher
Springer
Year
1993
Tongue
English
Weight
691 KB
Volume
44
Category
Article
ISSN
0044-2275

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๐Ÿ“œ SIMILAR VOLUMES


A critical exponent in a degenerate para
โœ Michael Winkler ๐Ÿ“‚ Article ๐Ÿ“… 2002 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 145 KB ๐Ÿ‘ 1 views

## Abstract We consider positive solutions of the Cauchy problem in \documentclass{article}\usepackage{amsfonts}\begin{document}\pagestyle{empty}$\mathbb{R\,}^n$\end{document} for the equation $$u\_t=u^p\,\Delta u+u^q,\quad p\geq1,\; q\geq 1$$\nopagenumbers\end and show that concerning global so

Critical Exponents of Quasilinear Parabo
โœ Yuan-Wei Qi; Ming-Xing Wang ๐Ÿ“‚ Article ๐Ÿ“… 2002 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 138 KB

In this paper we study the critical exponents of the Cauchy problem in R n of the quasilinear singular parabolic equations: u t = div โˆ‡u m-1 โˆ‡u + t s x ฯƒ u p , with non-negative initial data. Here s โ‰ฅ 0 n -1 / n + 1 < m < 1 p > 1 and ฯƒ > n 1 -m -1 + m + 2s . We prove that p c โ‰ก m + 1 + m + 2s + ฯƒ /n

The Critical Exponent of Doubly Singular
โœ Xinfeng Liu; Mingxin Wang ๐Ÿ“‚ Article ๐Ÿ“… 2001 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 147 KB

In this paper we study the Cauchy problem of doubly singular parabolic equations u t = div โˆ‡u ฯƒ โˆ‡u m + t s x ฮธ u p with non-negative initial data. Here -1 then every non-trivial solution blows up in finite time. But for p > p c a positive global solution exists.

Critical Exponents of Fujita Type for In
โœ C Bandle; H.A Levine; Qi S Zhang ๐Ÿ“‚ Article ๐Ÿ“… 2000 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 176 KB

We consider the large-time behavior of sign-changing solutions of inhomogeneous parabolic equations and systems. For example, for u t = u + u p + w x in R n ร— 0 T , we show the following: If n โ‰ฅ 3 and R n w x dx > 0 and 1 < p โ‰ค n/ n -2 , then all solutions blow up in finite time, while if p > n/ n -

Approximation of degenerate parabolic sy
โœ J. Kaฤur; S. Luckhaus ๐Ÿ“‚ Article ๐Ÿ“… 1998 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 912 KB

A degenerate, doubly nonlinear parabolic system is approximated by a nondegenerate one. The proposed type of approximation is effective from numerical point of view. The convergence of approximate solutions is proved for a rather general mathematical model.