Preprint No.
A-02-10
Jörg Härterich, Björn Sandstede, Arnd Scheel
Exponential dichotomies for linear non-autonomous functional
differential equations of mixed type
Abstract:
Functional differential equations with forward and backward delays
arise naturally, for instance, in the study of travelling waves in
lattice equations and as semi-discretizations of partial differential
equations (PDEs) on unbounded domains. Linear functional differential
equations of mixed type are typically ill-posed, i.e., there exists,
in general, no solution to a given initial condition. We prove that
Fredholm properties of these equations imply the existence of
exponential dichotomies. Exponential dichotomies can be used in
discretized PDEs and in lattice differential equations to construct
multi-pulses, to perform Evans-function type calculations, and to
justify numerical computations using artificial boundary conditions.
Keywords: Exponential dichotomy, semidiscretization, forward-backward
equation, completeness, Fredholm properties
Mathematics Subject Classification (MSC2000):
37L45, 37L60, 37C35, 34K25, 34K06
Language: ENG
Available: Pr-A-02-10.ps
Contact: Jörg Härterich, Freie Universität Berlin, Fachbereich Mathematik und Informatik, Arnimallee 2-6, D-14195 Berlin, Germany (haerter@math.fu-berlin.de)
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