A non-local population model of logistic type equation

TL;DR

This paper introduces a novel non-local logistic population model that preserves total population mass and demonstrates its global existence, stability, and long-term behavior in a bounded domain.

Contribution

It presents a new non-local logistic model with mass preservation and analyzes its global existence, stability, and asymptotic properties.

Findings

Model preserves the L^2 norm (mass) of solutions.

Solutions exist globally in time.

Solutions tend to a stable state asymptotically.

Abstract

In this paper, we propose a new non-local population model of logistic type equation on a bounded Lipschitz domain in the whole Euclidean space. This model preserves the L^2 norm, which is called mass, of the solution on the domain. We show that this model has the global existence, stability and asymptotic behavior at time infinity.