Parabolic equations with critical nonlinearities
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Global solutions, critical nonlinearity, Navier-Stokes systemAbstrakt
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.Pobrania
Opublikowane
2003-06-01
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1.
CHOLEWA, Jan W. & DŁOTKO, Tomasz. Parabolic equations with critical nonlinearities. Topological Methods in Nonlinear Analysis [online]. 1 czerwiec 2003, T. 21, nr 2, s. 311–324. [udostępniono 22.7.2024].
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