The principal eigenvalue problem for time-periodic nonlocal equations with drift

TL;DR

This paper establishes the existence and stability of a principal eigenvalue for a class of time-periodic nonlocal linear transport equations with an integral source, using spectral theory of positive operators.

Contribution

It introduces a novel approach to prove the existence of Floquet principal eigenvalues for nonlocal equations with periodic coefficients, expanding spectral theory applications.

Findings

Existence of a Floquet principal eigenvalue for the equation.

Nonnegative periodic solutions are exponentially attractive.

The method relies on spectral results for positive operators.

Abstract

In this work, we consider a general time-periodic linear transport equation with integral source term. We prove the existence of a Floquet principal eigenvalue, namely a real number such that the equation rescaled by this number admits nonnegative periodic solutions. We also prove the exponential attractiveness of these solutions. The method relies on general spectral results about positive operators.