Paper Info
Title
First and Second Order Semistrong Interaction in Reaction-Diffusion Systems.
Abstract
Spatial scale separation often leads to sharp interfaces that can be fully localized pulses or transition layer fronts connecting different states. This paper concerns the asymptotic interaction laws of pulses and fronts in the so-called semistrong regime of strongly differing diffusion lengths for reaction-diffusion systems in one space dimension. An asymptotic expansion and matching approach is applied in a model independent common framework. First order semistrong interaction is introduced as a general interface interaction type. It is distinct from the semistrong interaction studied over the past decade, which is referred to as "second order" here. Laws of motion are derived for pulses as well as fronts in abstract systems with attention to the effect of symmetries. First order interaction for pulses is shown to be gradient-like under conditions that are numerically checked for a class of equations including the Gray-Scott and Schnakenberg models.
Year
DOI
Venue
2013
10.1137/110850165
SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS
Keywords
Field
DocType
reaction-diffusion systems,pulses and fronts,asymptotic expansion,transition layers,sharp interfaces,slow invariant manifold,Lyapunov functional
Newton's laws of motion,Mathematical analysis,First order,Asymptotic expansion,Reaction–diffusion system,Lyapunov functional,Mathematics,Homogeneous space
Journal
Volume
Issue
ISSN
12
1
1536-0040
Citations 
PageRank 
References 
3
0.60
4
Authors
1
Name
Order
Citations
PageRank
Jens D. M. Rademacher1165.06