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Propagation of hexagonal patterns near onset

Published online by Cambridge University Press:  17 March 2003

ARJEN DOELMAN ,
BJÖRN SANDSTEDE ,
ARND SCHEEL  and
GUIDO SCHNEIDER
ARJEN DOELMAN
Affiliation:
Korteweg–de Vries Institute, University of Amsterdam, Plantage Muidergracht 24, 1018 TV Amsterdam, The Netherlands
BJÖRN SANDSTEDE
Affiliation:
Department of Mathematics, The Ohio State University, 231 West 18th Avenue, Columbus, OH 43210, USA
ARND SCHEEL
Affiliation:
Department of Mathematics, University of Minnesota, 127 Vincent Hall, 206 Church St. S.E., Minneapolis, MN 55455, USA
GUIDO SCHNEIDER
Affiliation:
Mathematisches Institut I, Universität Karlsruhe, 76128 Karlsruhe, Germany
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Abstract

For a pattern-forming system with two unbounded spatial directions that is near the onset to instability, we prove the existence of modulated fronts that connect (i) stable hexagons with the unstable trivial pattern, (ii) stable hexagons with unstable roll solutions, (iii) stable hexagons with unstable hexagons, and (iv) stable roll solutions with unstable hexagons. Our approach is based on spatial dynamics, bifurcation theory, and geometric singular perturbation theory.

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 14 , Issue 1 , February 2003 , pp. 85 - 110
Copyright
2003 Cambridge University Press

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