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.
Recommended Citation
Lindstrom, Michael R., and Andrea L. Bertozzi. "Qualitative features of a nonlinear, nonlocal, agent-based PDE model with applications to homelessness." Mathematical Models and Methods in Applied Sciences 30, no. 10 (2020): 1863-1891. https://doi.org/10.1142/S0218202520400114
Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.
Publication Title
Mathematical Models and Methods in Applied Sciences
DOI
10.1142/S0218202520400114
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.