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Izv. IMI UdGU, 2015, Issue 2(46), Pages 60–68 (Mi iimi303)  

Stability and bifurcations of undulate solutions for one functional-differential equation

A. M. Kovaleva, A. N. Kulikov, D. A. Kulikov

P.G. Demidov Yaroslavl State University, ul. Sovetskaya, 14, Yaroslavl, 150000, Russia

Abstract: A periodic boundary-value problem for one nonlinear functional-differential equation is considered. This equation is well known as the nonlocal erosion equation. The case of small spatial deviation is studied. The possibility of the bifurcations for the spatial nonhomogeneous solutions is demonstrated. For these solutions, the asymptotical formulas are obtained and the stability is studied. All results are obtained with the help of the bifurcation theory.

Keywords: nonlocal model of erosion, normal forms, stability, bifurcations, asymptotic formulas.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation МК-5932.2015.1


Full text: PDF file (275 kB)
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UDC: 517.956.4, 51-73
MSC: 34K18, 34K19, 34K20
Received: 14.10.2015

Citation: A. M. Kovaleva, A. N. Kulikov, D. A. Kulikov, “Stability and bifurcations of undulate solutions for one functional-differential equation”, Izv. IMI UdGU, 2015, no. 2(46), 60–68

Citation in format AMSBIB
\Bibitem{KovKulKul15}
\by A.~M.~Kovaleva, A.~N.~Kulikov, D.~A.~Kulikov
\paper Stability and bifurcations of undulate solutions for one functional-differential equation
\jour Izv. IMI UdGU
\yr 2015
\issue 2(46)
\pages 60--68
\mathnet{http://mi.mathnet.ru/iimi303}
\elib{http://elibrary.ru/item.asp?id=25030024}


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