School of Mathematical and Statistical Sciences Faculty Publications and Presentations

Document Type

Article

Publication Date

9-26-2020

Abstract

In this paper, we develop a continuum model for the movement of agents on a lattice, taking into account location desirability, local and far-range migration, and localized entry and exit rates. Specifically, our motivation is to qualitatively describe the homeless population in Los Angeles. The model takes the form of a fully nonlinear, nonlocal, non-degenerate parabolic partial differential equation. We derive the model and prove useful properties of smooth solutions, including uniqueness and L2 -stability under certain hypotheses. We also illustrate numerical solutions to the model and find that a simple model can be qualitatively similar in behavior to observed homeless encampments.

Comments

© The Author(s)

This is an Open Access article published by World Scientific Publishing Company. It is distributed under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 (CC BY-NC-ND) License which permits use, distribution and reproduction, provided that the original work is properly cited, the use is non-commercial and no modifications or adaptations are made.

Publication Title

Mathematical Models and Methods in Applied Sciences

DOI

10.1142/S0218202520400114

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