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Pointwise stability of reaction diffusion fronts

Published online by Cambridge University Press:  25 March 2019

Yingwei Li*
Affiliation:
Indiana University, 831 East Third Street, Rawles Hall, Bloomington, Indiana47405, USA ([email protected])

Abstract

Using pointwise semigroup techniques, we establish sharp rates of decay in space and time of a perturbed reaction diffusion front to its time-asymptotic limit. This recovers results of Sattinger, Henry and others of time-exponential convergence in weighted Lp and Sobolev norms, while capturing the new feature of spatial diffusion at Gaussian rate. Novel features of the argument are a pointwise Green function decomposition reconciling spectral decomposition and short-time Nash-Aronson estimates and an instantaneous tracking scheme similar to that used in the study of stability of viscous shock waves.

MSC classification

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 2019

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