On the global behaviour of solutions of some fourth order nonlinear equations
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 19, Tome 163 (1987), pp. 66-75
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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.
@article{ZNSL_1987_163_a5,
author = {V. K. Kalantarov},
title = {On the global behaviour of solutions of some fourth order nonlinear equations},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {66--75},
publisher = {mathdoc},
volume = {163},
year = {1987},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_1987_163_a5/}
}
V. K. Kalantarov. On the global behaviour of solutions of some fourth order nonlinear equations. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 19, Tome 163 (1987), pp. 66-75. http://geodesic.mathdoc.fr/item/ZNSL_1987_163_a5/