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Qualitative features of a nonlinear, nonlocal, agent-based PDE model with applications to homelessness.
- Source :
-
Mathematical Models & Methods in Applied Sciences . Sep2020, Vol. 30 Issue 10, p1863-1891. 29p. - Publication Year :
- 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 L 2 -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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 02182025
- Volume :
- 30
- Issue :
- 10
- Database :
- Academic Search Index
- Journal :
- Mathematical Models & Methods in Applied Sciences
- Publication Type :
- Academic Journal
- Accession number :
- 146510419
- Full Text :
- https://doi.org/10.1142/S0218202520400114