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Evans function and blow-u[ methods in critical eienvalue problems

Sandstede, B. and Scheel, A, (2004) Evans function and blow-u[ methods in critical eienvalue problems Discrete and Continuous Dynamical Systems, 10 (2004).

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Abstract

Contact defects are one of several types of defects that arise generically in oscillatory media modelled by reaction-diffusionsystems. An interesting property of these defects is that the asymptotic spatial wave number is approached only with algebraic order O(1/x) (the associated phase diverges logarithmically). The essential spectrum of the PDE linearization about a contact defect always has a branch point at the origin. We show that the Evans function can be extended across this branch point and discuss the smoothness properties of the extension. The construction utilizes blow-up techniques and is quite general in nature. We also comment on known relations between roots of the Evans function and the temporal asymptotics of Green’s functions, and discuss applications to algebraically decaying solitons.

Item Type: Article
Additional Information: Discrete and Continuous Dynamical Systems 10 (2004) 941-964
Uncontrolled Keywords: nonlinear waves, dissipative, pattern-forming partial differential equations
Divisions: Faculty of Engineering and Physical Sciences > Mathematics
Depositing User: Mr Adam Field
Date Deposited: 27 May 2010 14:41
Last Modified: 23 Sep 2013 18:33
URI: http://epubs.surrey.ac.uk/id/eprint/1525

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