In this paper, we propose a new non-local population model, which is of logistic type equation on a bounded Lipschitz domain in the whole Euclidean space. This model preserves the L2 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.
Cheng, Liang and Ma, Li, "Report on the Lp Non-local Flow and its Application to Population Model" (2009). ICEB 2009 Proceedings. 141.