## 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 exponent for a quasilinear parabolic equation with inhomogeneous density in a cone
โ Scribed by Changchun Liu
- Publisher
- Springer Vienna
- Year
- 2010
- Tongue
- English
- Weight
- 175 KB
- Volume
- 165
- Category
- Article
- ISSN
- 0026-9255
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
We study solutions to the Cauchy problem for a semilinear parabolic equation with a nonlinearity which is critical in the sense of Joseph and Lundgren and establish the rate of convergence to regular steady states. In the critical case, this rate contains a logarithmic term which does not appear in
It is shown that there exists a critical exponent p \* > 1 for the bipolar blowup in the following sense. If 1 < p โค p \* , then there exist arbitrarily small initial data such that the solution exhibits the bipolar blowup, whereas if p > p \* , then the bipolar blowup does not occur for any suffici