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

Authors

Michael R. Lindstrom, The University of Texas Rio Grande ValleyFollow

Document Type

Article

Publication Date

5-2024

Abstract

Highlights

• 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

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.

Comments

Original published version available at https://doi.org/10.1016/j.cnsns.2024.107815

Recommended Citation

Lindstrom, Michael R. "Local existence of solutions to a nonlinear autonomous PDE model for population dynamics with nonlocal transport and competition." Communications in Nonlinear Science and Numerical Simulation (2024): 107815. https://doi.org/10.1016/j.cnsns.2024.107815

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.

Publication Title

Communications in Nonlinear Science and Numerical Simulation

DOI

10.1016/j.cnsns.2024.107815