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Zapiski Nauchnykh Seminarov LOMI, 1987, Volume 163, Pages 66–75
(Mi znsl5458)
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This article is cited in 3 scientific papers (total in 3 papers)
On the global behaviour of solutions of some fourth order nonlinear equations
V. K. Kalantarov
Abstract:
Zbere are considered two classes of fourth order nonlinear
evolution equations, for first class, included the well known
Hahn–Hillard equation, it is proved that there exists a global
minimal $B$-attractor, and it is compact and connected, for the second
class, included Sivashinsky equation, it is proved a blow-up
theorem. In addition, for the Kuramoto–Sivashinsky equation, in
one-dimensional case, for even solutions it is prouved the existence
of a global minimal $B$-attractor in the fase-space $W_2^1$.
Xhis attraetor is compact and connected. In the multi-dimensional
case $(n=2,3)$ under some assumption, it is proved the existence
of compact attractors for some bounded sets.
Citation:
V. K. Kalantarov, “On the global behaviour of solutions of some fourth order nonlinear equations”, Boundary-value problems of mathematical physics and related problems of function theory. Part 19, Zap. Nauchn. Sem. LOMI, 163, "Nauka", Leningrad. Otdel., Leningrad, 1987, 66–75
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https://www.mathnet.ru/eng/znsl5458 https://www.mathnet.ru/eng/znsl/v163/p66
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Abstract page: | 146 | Full-text PDF : | 62 |
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