MATEMATIČKI VESNIKVol. 70, No. 1, pp. 26–39 (2018)
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MATEMATIČKI VESNIK Vol. 70, No. 1, pp. 26–39 (2018) |
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Initial–boundary value problems for Fuss-Winkler-Zimmermann and Swift–Hohenberg nonlinear equations of 4th orderD. KostinVoronezh State University, Universitetskaya pl. 1, Voronezh, Russia, 394018; RUDN University, 6 Miklukho-Maklay st., Moscow, Russia, 117198 E-mail: dvk605@mail.ruKeywords: This paper presents results of the investigation of bifurcations of stationary solutions of the Swift–Hohenberg equation and dynamic descent to the points of minimal values of the functional of energy for this equation, obtained with the use of the modification of the Lyapunov–Schmidt variation method and some methods from the theory of singularities of smooth functions. Nonstationary case is investigated by the construction of paths of descent along the trajectories of the infinite-dimensional SH dynamical system from arbitrary initial states to points of the minimum energy. Classification (MSC2000): 37M20; 35Q99, 34K18, 34C25 Full text of the article: (for faster download, first choose a mirror)
Electronic fulltext finalized on: 16 Dec 2017. This page was last modified: 11 Mai 2018.
© 2017 Mathematical Society of Serbia (Društvo matematičara Srbije)
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