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Pointwise stability of reaction diffusion fronts

Part of: Parabolic equations and systems

Published online by Cambridge University Press:  25 March 2019

Yingwei Li
Yingwei Li*
Affiliation:
Indiana University, 831 East Third Street, Rawles Hall, Bloomington, Indiana47405, USA (YL37@umail.iu.edu)
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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.

Keywords

pointwise semigroup methodreaction diffusion equationnonlinear stability

MSC classification

Primary: 35K57: Reaction-diffusion equations
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 150 , Issue 5 , October 2020 , pp. 2216 - 2254
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Copyright
Copyright © Royal Society of Edinburgh 2019

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