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Qualitative features of a nonlinear, nonlocal, agent-based PDE model with applications to homelessness
Mathematical Models and Methods in Applied Sciences ( IF 3.5 ) Pub Date : 2020-09-13 , DOI: 10.1142/s0218202520400114
Michael R. Lindstrom 1 , Andrea L. Bertozzi 1, 2
Affiliation  

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 [Formula: see text]-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.

中文翻译:

非线性、非局部、基于代理的 PDE 模型的定性特征,适用于无家可归者

在本文中,我们开发了一个网格上代理移动的连续模型,考虑了位置可取性、本地和远距离迁移以及本地化的进入和退出率。具体来说,我们的动机是定性地描述洛杉矶的无家可归人口。该模型采用完全非线性、非局部、非退化抛物线偏微分方程的形式。我们推导出模型并证明平滑解的有用属性,包括唯一性和 [公式:见文本] - 在某些假设下的稳定性。我们还说明了模型的数值解,并发现一个简单的模型在行为上与观察到的无家可归者营地的行为在性质上相似。
更新日期:2020-09-13
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