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Session S18 - Recent progress in non-linear PDEs and their applications

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Nonlocal PDEs in Ecology

Erin Ellefsen

University of Colorado Boulder, United States   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

Nonlocal models can be very useful to describe some phenomena in Ecology. However, they also pose both analytical and computational challenges. We investigate territory development of meerkats by studying a system of nonlocal continuum equations, and we take advantage of the gradient-flow structure of the system in order to find equilibrium solutions. We first find explicit equilibrium solutions of the model. We then perform a long-wave approximation of this system to investigate a local approximation. We compare the equilibrium solutions of the local and nonlocal models to determine if the local model is an appropriate approximation for future work. Finally, we explore finding equilibrium solutions of the system using spectral methods.

Joint work with Nancy Rodriguez (University of Colorado Boulder).

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