Journal of Soviet Mathematics

, Volume 49, Issue 5, pp 1160–1166 | Cite as

Global behavior of the solutions of certain fourth-order nonlinear equations

  • V. K. Kalantarov

Abstract

Two classes of fourth-order nonlinear evolution equations are considered. For the first class of equations, including the known Cahn-Hilliard equation, it is proved that there exists a global minimal B-attractor; it is compact and connected. For the second class, one of the representatives of which is the Sivashinsky equation, a theorem regarding the blowup of the solutions in finite time is proved. In addition, for the Kuramoto-Sivashinsky equation, in the one-dimensional case, the existence of a global minimal B-attractor from W21 in the class of even functions is proved. This attractor is compact and connected. In the multidimensional case (n=2, 3) a conditional theorem is proved regarding the existence of a compact attractor.

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© Plenum Publishing Corporation 1990

Authors and Affiliations

  • V. K. Kalantarov

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