Parabolic equations with critical nonlinearities
Keywords
Global solutions, critical nonlinearity, Navier-Stokes systemAbstract
As well known the problem of global continuation of solutions to semilinear parabolic equations is completely solved when the nonlinear term is subordinated to an $\alpha$-power of the main linear operator with $\alpha\in[0,1)$. In this paper we study three examples of {\it critical problems} in which the mentioned subordination takes place with $\alpha=1$, i.e. the nonlinearity has the same {\it order of magnitude} as the linear main part. We use specific techniques of proving global solvability that fit well the considered examples for which general abstract methods fail.Downloads
Published
2003-06-01
How to Cite
1.
CHOLEWA, Jan W. and DŁOTKO, Tomasz. Parabolic equations with critical nonlinearities. Topological Methods in Nonlinear Analysis. Online. 1 June 2003. Vol. 21, no. 2, pp. 311 - 324. [Accessed 29 March 2024].
Issue
Section
Articles
Stats
Number of views and downloads: 0
Number of citations: 0