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Your search keyword '"Lindstrom, Michael R."' showing total 2 results
Start Over Author "Lindstrom, Michael R." Topic nonlinear diffusion
2 results on '"Lindstrom, Michael R."'

1. Qualitative features of a nonlinear, nonlocal, agent-based PDE model with applications to homelessness

Author

Lindstrom, Michael R and Bertozzi, Andrea L

Subjects
Agent-based model, nonlocal PDE, nonlinear diffusion, solution properties, homelessness, Applied Mathematics, Numerical and Computational Mathematics
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 [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.

Published
2020

2. Local existence of solutions to a nonlinear autonomous PDE model for population dynamics with nonlocal transport and competition.

Author

Lindstrom, Michael R.

Subjects
*PARABOLIC differential equations, *LOTKA-Volterra equations, *PARTIAL differential equations, *CLASSICAL solutions (Mathematics), *APPLIED sciences, *MASS transfer
Abstract

In this paper, we prove that a particular nondegenerate, nonlinear, autonomous parabolic partial differential equation with nonlocal mass transfer admits the local existence of classical solutions. The equation was developed to qualitatively describe temporal changes in population densities over space through accounting for location desirability and fast, long-range travel. Beginning with sufficiently regular initial conditions, through smoothing the PDE and employing energy arguments, we obtain a sequence of approximators converging to a classical solution. • Partial differential equation models are ubiquitous in applied sciences. • A partial differential equation based in ecology is studied for solution existence. • Energy methods and convergence analysis lead to local classical solutions. [ABSTRACT FROM AUTHOR]

Published
2024
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