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Local dynamics of two-component singularly perturbed parabolic systems


Authors: I. S. Kashchenko and S. A. Kashchenko
Translated by: E. Khukhro
Original publication: Trudy Moskovskogo Matematicheskogo Obshchestva, tom 77 (2016), vypusk 1.
Journal: Trans. Moscow Math. Soc. 2016, 55-68
MSC (2010): Primary 35K67; Secondary 35B10, 35B25, 35C20, 35K40
DOI: https://doi.org/10.1090/mosc/252
Published electronically: November 28, 2016
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Abstract | References | Similar Articles | Additional Information

Abstract: We consider the local dynamics in a neighbourhood of a stationary state of a two-component system of parabolic equations with periodic boundary conditions. In the critical cases we construct families of special equations--quasinormal forms whose solutions in principle give asymptotic solutions, up to the residual, of the original singularly perturbed system.


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Additional Information

I. S. Kashchenko
Affiliation: Yaroslavl’ State University
Email: iliyask@uniyar.ac.ru

S. A. Kashchenko
Affiliation: Yaroslavl’ State University, National Research Nuclear University (Moscow Engineering Physics Institute)
Email: kasch@uniyar.ac.ru

DOI: https://doi.org/10.1090/mosc/252
Keywords: Parabolic equation, quasinormal form, small parameter.
Published electronically: November 28, 2016
Additional Notes: This research was supported by project no. 984 within the framework of the basic part of the state programme for scientific research of Yaroslavl’ State University and a grant from the President of the Russian Federation (contract no. 14.124.13.5948-MK)
Article copyright: © Copyright 2016 American Mathematical Society