Geodesic
Bifurcations of Spatially Inhomogeneous Solutions in Two Versions of the Nonlocal Erosion Equation
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference “Geometric Methods in Control Theory and Mathematical Physics: Differential Equations, Integrability, and Qualitative Theory,” Ryazan, September 15–18, 2016, Tome 148 (2018), pp. 66-74

Voir la notice de l'article provenant de la source Math-Net.Ru

A periodic boundary-value problem for two versions of the nonlocal erosion equation is considered. This equation belongs to the class of partial differential equations with deviating spatial arguments. The issue of bifurcations of spatially inhomogeneous solutions is studied for the periodic boundary-value problem. In order to study the problem, we use the method of integral manifolds and normal forms.
Keywords: partial differential equations with deviating spatial argument, periodic boundary value problem, stability, asymptotic formulas.
Mots-clés : bifurcations 
@article{INTO_2018_148_a8,
     author = {A. M. Kovaleva and D. A. Kulikov},
     title = {Bifurcations of {Spatially} {Inhomogeneous} {Solutions} in {Two} {Versions} of the {Nonlocal} {Erosion} {Equation}},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {66--74},
     publisher = {mathdoc},
     volume = {148},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2018_148_a8/}
}
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A. M. Kovaleva; D. A. Kulikov. Bifurcations of Spatially Inhomogeneous Solutions in Two Versions of the Nonlocal Erosion Equation. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference “Geometric Methods in Control Theory and Mathematical Physics: Differential Equations, Integrability, and Qualitative Theory,” Ryazan, September 15–18, 2016, Tome 148 (2018), pp. 66-74. http://geodesic.mathdoc.fr/item/INTO_2018_148_a8/