Point-wise Stability of Reaction Diffusion Fronts

2016/02/26 by Yingwei Li, Li, Yingwei
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP

paper · pdf · doi:10.48550/arxiv.1602.08176

arXiv admin note: substantial text overlap with arXiv:1004.0909 by other authors

arxiv created 2019/01/13 · arxiv updated 2019/01/15

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 L^p and Sobolev norms, while capturing the new feature of spatial diffusion at Gaussian rate. Novel features of the argument are a point-wise 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.

Citations

• Nonlinear stability of spatially-periodic traveling-wave solutions of systems of reaction diffusion equations

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