Road-field reaction-diffusion system: a new threshold for long range exchanges
Antoine Pauthier
TL;DR
This paper investigates reaction-diffusion equations with a fast diffusion line and non-local exchange, revealing a new threshold in long-range exchange terms that affects the propagation speed.
Contribution
It introduces a novel threshold phenomenon in the influence of long-range exchange terms on the spreading speed in reaction-diffusion systems.
Findings
Identifies a new threshold in long-range exchange limit
Shows the line's influence depends on exchange function range
Analyzes the infimum of spreading speed in the system
Abstract
We consider reaction-diffusion equations of KPP type in a presence of a line of fast diffusion with non-local exchange terms between the line and the framework. Our study deals with the infimum of the spreading speed depending on the exchange functions. We exhibit a new threshold in the limit of long range exchange terms for the line to influence the propagation.
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Taxonomy
TopicsMathematical and Theoretical Epidemiology and Ecology Models · Nonlinear Dynamics and Pattern Formation · Advanced Mathematical Modeling in Engineering