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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2018, Volume 148, Pages 66–74 (Mi into304)  
This article is cited in 2 scientific papers (total in 2 papers)

Bifurcations of Spatially Inhomogeneous Solutions in Two Versions of the Nonlocal Erosion Equation

A. M. Kovaleva, D. A. Kulikov

P.G. Demidov Yaroslavl State University
Full-text PDF (199 kB) Citations (2)
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Abstract: 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, bifurcations, asymptotic formulas.
English version:
Journal of Mathematical Sciences (New York), 2020, Volume 248, Issue 4, Pages 438–447
DOI: https://doi.org/10.1007/s10958-020-04884-0
Bibliographic databases:
Document Type: Article
UDC: 517.929
MSC: 34K18, 34K19
Language: Russian
Citation: A. M. Kovaleva, D. A. Kulikov, “Bifurcations of Spatially Inhomogeneous Solutions in Two Versions of the Nonlocal Erosion Equation”, Proceedings of the International Conference “Geometric Methods in Control Theory and Mathematical Physics: Differential Equations, Integrability, and Qualitative Theory,” Ryazan, September 15–18, 2016, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 148, VINITI, M., 2018, 66–74; J. Math. Sci. (N. Y.), 248:4 (2020), 438–447
Citation in format AMSBIB
\Bibitem{KovKul18}
\by A.~M.~Kovaleva, D.~A.~Kulikov
\paper Bifurcations of Spatially Inhomogeneous Solutions in Two Versions of the Nonlocal Erosion Equation
\inbook Proceedings of the International Conference ``Geometric Methods in Control Theory and Mathematical Physics: Differential Equations, Integrability, and Qualitative Theory,'' Ryazan, September 15--18, 2016
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2018
\vol 148
\pages 66--74
\publ VINITI
\publaddr M.
\mathnet{http://mi.mathnet.ru/into304}
\mathscinet{https://mathscinet.ams.org/mathscinet-getitem?mr=3847709}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2020
\vol 248
\issue 4
\pages 438--447
\crossref{https://doi.org/10.1007/s10958-020-04884-0}
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