Geodesic
Bifurcations in Kuramoto--Sivashinsky equations
Teoretičeskaâ i matematičeskaâ fizika, Tome 192 (2017) no. 1, pp. 23-40

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We consider the local dynamics of the classical Kuramoto–Sivashinsky equation and its generalizations and study the problem of the existence and asymptotic behavior of periodic solutions and tori. The most interesting results are obtained in the so-called infinite-dimensional critical cases. Considering these cases, we construct special nonlinear partial differential equations that play the role of normal forms and whose nonlocal dynamics thus determine the behavior of solutions of the original boundary value problem.
Mots-clés : bifurcation, singular perturbation
Keywords: stability, normal form, dynamics. 
@article{TMF_2017_192_1_a1,
     author = {S. A. Kashchenko},
     title = {Bifurcations in {Kuramoto--Sivashinsky} equations},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {23--40},
     publisher = {mathdoc},
     volume = {192},
     number = {1},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2017_192_1_a1/}
}
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S. A. Kashchenko. Bifurcations in Kuramoto--Sivashinsky equations. Teoretičeskaâ i matematičeskaâ fizika, Tome 192 (2017) no. 1, pp. 23-40. http://geodesic.mathdoc.fr/item/TMF_2017_192_1_a1/