A Note on a Nonlocal Nonlinear Reaction-Diffusion Model
Christoph Walker
TL;DR
This paper applies bifurcation theory to analyze steady-state solutions of a nonlocal nonlinear reaction-diffusion system modeling interacting age-structured populations.
Contribution
It introduces a novel application of the Crandall-Rabinowitz theorem to a complex nonlocal reaction-diffusion model with cross-diffusion and nonlocal initial conditions.
Findings
Identification of bifurcation points in the model
Existence of nontrivial steady states
Insights into population interaction dynamics
Abstract
We give an application of the Crandall-Rabinowitz theorem on local bifurcation to a system of nonlinear parabolic equations with nonlocal reaction and cross-diffusion terms as well as nonlocal initial conditions. The system arises as steady-state equations of two interacting age-structured populations.
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Taxonomy
TopicsMathematical and Theoretical Epidemiology and Ecology Models · Nonlinear Differential Equations Analysis · Mathematical Biology Tumor Growth