Transition Fronts in Inhomogeneous Fisher-KPP Reaction-Diffusion Equations
Andrej Zlatos
TL;DR
This paper introduces a novel method for establishing the existence of transition fronts in inhomogeneous Fisher-KPP reaction-diffusion equations, providing new estimates for solutions across multiple spatial dimensions.
Contribution
It presents a new approach using sub- and super-solutions derived from linearization to prove transition fronts in inhomogeneous KPP equations, advancing theoretical understanding.
Findings
Existence of transition fronts in one-dimensional inhomogeneous KPP equations.
New estimates on entire solutions in higher spatial dimensions.
Method based on linearization at zero for constructing solutions.
Abstract
We use a new method in the study of Fisher-KPP reaction-diffusion equations to prove existence of transition fronts for inhomogeneous KPP-type non-linearities in one spatial dimension. We also obtain new estimates on entire solutions of some KPP reaction-diffusion equations in several spatial dimensions. Our method is based on the construction of sub- and super-solutions to the non-linear PDE from solutions of its linearization at zero.
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Taxonomy
TopicsMathematical and Theoretical Epidemiology and Ecology Models · Nonlinear Differential Equations Analysis · Differential Equations and Numerical Methods