Geodesic
Bifurcations of spatially inhomogeneous solutions in a modified version of the Kuramoto--Sivashinsky equation
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the All-Russian Scientific Conference «Differential Equations and Their Applications» dedicated to the 85th anniversary of Professor M.T.Terekhin. Ryazan State University named for S.A. Yesenin, Ryazan, May 17-18, 2019. Part 1, Tome 185 (2020), pp. 58-71.

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A periodic boundary-value problem for an equation with a deviating spatial argument is considered. Using the Poincaré–Dulac method of normal forms, the method of integral manifolds, and asymptotic formulas, we examine a number of bifurcation problems of codimension $1$ and $2$. For homogeneous equilibrium states, we analyze possibilities of realizing critical cases of various types. The problem on the stability of homogeneous equilibrium states is studied and asymptotic formulas for spatially inhomogeneous solutions and conditions for their stability are obtained.
Keywords: functional differential equation, periodic boundary-value problem, stability, asymptotics, Kuramoto–Sivashinsky equation.
Mots-clés : bifurcation 
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     author = {A. M. Kovaleva},
     title = {Bifurcations of spatially inhomogeneous solutions in a modified version of the {Kuramoto--Sivashinsky} equation},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {58--71},
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A. M. Kovaleva. Bifurcations of spatially inhomogeneous solutions in a modified version of the Kuramoto--Sivashinsky equation. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the All-Russian Scientific Conference «Differential Equations and Their Applications» dedicated to the 85th anniversary of Professor M.T.Terekhin. Ryazan State University named for S.A. Yesenin, Ryazan, May 17-18, 2019. Part 1, Tome 185 (2020), pp. 58-71. http://geodesic.mathdoc.fr/item/INTO_2020_185_a6/

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