The steady states of strong-KPP reactions in general domains

TL;DR

This paper investigates the uniqueness of positive steady states in strong-KPP reaction-diffusion equations across various domains, establishing conditions for uniqueness and proposing open problems.

Contribution

It introduces spectral nondegeneracy conditions ensuring uniqueness of steady states in general domains for strong-KPP equations.

Findings

Positive bounded steady states are unique under spectral nondegeneracy.

The paper formulates open problems and conjectures in the field.

Provides conditions for uniqueness in general domains.

Abstract

We study the uniqueness of steady states of strong-KPP reaction--diffusion equations in general domains under various boundary conditions. We show that positive bounded steady states are unique provided the domain satisfies a certain spectral nondegeneracy condition. We also formulate a number of open problems and conjectures.