Ihsan Topaloglu

Swarming in domains with boundaries: approximation and regularization by nonlinear diffusion

Date: 2/23/2018
Time: 3:00PM-4:00PM
Place: 422 Armstrong Hall

Abstract: In this talk I will consider an aggregation model with nonlinear diffusion in domains with boundaries and present on the zero diffusion limit of its solutions. This model is used in describing phenomena related swarming and social aggregations, such as biological swarms and pattern formation, granular media, and self-assembly of nanoparticles. Using the formulation of the aggregation model as a gradient flow on spaces of probability measures equipped with the Wasserstein metric, I will present the convergence of weak solutions for fixed times, as well as the convergence of energy minimizers in this limit. I will also present numerical simulations that support the analytical results and demonstrates that adding small nonlinear diffusion approximates, as well as regularizes, the plain aggregation model. This is a joint project with Razvan Fetacau and Mitchell Kovacic.

Ihsan Topaloglu

All are welcome.

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