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Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, 2015, Issue 2(46), Pages 60–68
(Mi iimi303)
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This article is cited in 2 scientific papers (total in 2 papers)
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.
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
Linking options:
https://www.mathnet.ru/eng/iimi303 https://www.mathnet.ru/eng/iimi/y2015/i2/p60
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Abstract page: | 171 | Full-text PDF : | 74 | References: | 51 |
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