Geodesic
Structures of a parabolic problem with transformation of a spatial variable
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 2, Tome 186 (2020), pp. 138-143

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A nonlinear parabolic equation with transformation of the spatial variable and periodic conditions on the circle is considered. Using the method of separation of variables, we obtain properties of eigenfunctions and eigenvalues of the corresponding linearized problem. Using the method of central manifolds, we prove the existence and stability of spatially inhomogeneous stationary solutions. Based on the Galerkin method, we analyze approximate solutions of the original problem.
Mots-clés : parabolic equation, bifurcation
Keywords: method of central manifolds, stability, Galerkin method. 
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     author = {Yu. A. Khazova and Yu. D. Likhogrud},
     title = {Structures of a parabolic problem with transformation of a spatial variable},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {138--143},
     publisher = {mathdoc},
     volume = {186},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2020_186_a17/}
}
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Yu. A. Khazova; Yu. D. Likhogrud. Structures of a parabolic problem with transformation of a spatial variable. 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 2, Tome 186 (2020), pp. 138-143. http://geodesic.mathdoc.fr/item/INTO_2020_186_a17/