Spatial segregation limit of traveling wave solutions for a fully nonlinear strongly coupled competitive system
L\'eo Girardin (ICJ, CNRS), Danielle Hilhorst (LMO, CNRS)
TL;DR
This paper investigates the behavior of traveling wave solutions in complex nonlinear two-species systems, deriving a limiting free boundary problem that characterizes their segregation limits under certain conditions.
Contribution
It introduces a new analysis of the singular limit for fully nonlinear competitive systems, providing a detailed characterization of the limiting free boundary problem.
Findings
Derivation of the limiting free boundary problem
Characterization of the segregation limit
Application to important biological models
Abstract
The paper is concerned with a singular limit for the bistable traveling wave problem in a very large class of two-species fully nonlinear parabolic systems with competitive reaction terms. Assuming existence of traveling waves and enough compactness, we derive and characterize the limiting problem. The assumptions and results are discussed in detail. The free boundary problem obtained at the limit is specified for important applications.
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Taxonomy
TopicsMathematical and Theoretical Epidemiology and Ecology Models · Nonlinear Partial Differential Equations · Nonlinear Differential Equations Analysis