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Bifurcation Theory for Dissipative Systems on Unbounded Cylindrical Domains — An Introduction to the Mathematical Theory of Modulation Equations —
Author(s) -
Schneider G.
Publication year - 2001
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/1521-4001(200108)81:8<507::aid-zamm507>3.0.co;2-1
Subject(s) - dissipative system , bifurcation theory , bifurcation , modulation (music) , mathematics , mathematical analysis , mathematical theory , physics , classical mechanics , nonlinear system , thermodynamics , quantum mechanics , acoustics
In this introductory text we consider dissipative translational invariant nonlinear partial differential equations posed on spatially unbounded cylindrical domains close to the threshold of instability. We give an overview about the mathematical theory of modulation equations which allows us to analyse bifurcation problems occurring in such systems. We explain this theory by presenting new results concerning the dynamics of interface solutions bifurcating in certain reaction‐diffusion systems.