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Contemporary Mathematics. Fundamental Directions, 2013, Volume 47, Pages 60–77
(Mi cmfd223)
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Localized solutions of a piecewise linear model of the stationary Swift–Hohenberg equation on the line and on the plane
N. E. Kulagina, L. M. Lermanbc a State University of Management, Moscow, Russia
b Research Institute for Applied Mathematics and Cybernetics, Lobachevski Nizhnii Novgorod State University, Nizhnii Novgorod, Russia
c Lobachevski Nizhni Novgorod State University, Faculty of Mechanics
and Mathematics, Nizhni Novgorod, Russia
Abstract:
In this paper we study a simplified model of the stationary Swift–Hohenberg equation, where the cubic nonlinearity is replaced by a piecewise linear function with similar properties. The main goal is to prove the existence of so-called localized solutions of this equation, i.e., solutions decaying to a homogeneous zero state with unbounded increase of the space variable. The following two cases of the space variable are considered: one-dimensional (on the whole line) and two-dimensional; in the latter case, radially symmetric solutions are studied. The existence of such solutions and increase of their number with change in the equation parameters are shown.
Citation:
N. E. Kulagin, L. M. Lerman, “Localized solutions of a piecewise linear model of the stationary Swift–Hohenberg equation on the line and on the plane”, Proceedings of the Sixth International Conference on Differential and Functional-Differential Equations (Moscow, August 14–21, 2011). Part 3, CMFD, 47, PFUR, M., 2013, 60–77; Journal of Mathematical Sciences, 202:5 (2014), 684–702
Linking options:
https://www.mathnet.ru/eng/cmfd223 https://www.mathnet.ru/eng/cmfd/v47/p60
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Abstract page: | 240 | Full-text PDF : | 66 | References: | 33 |
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