## 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
The critical exponent of degenerate parabolic systems
โ 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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๐ SIMILAR VOLUMES
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
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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.