On Nonlocal Keller-Segel Type Equations (April 2017)
The Department of Mathematics and Statistics at the College of Arts and Sciences (CAS) invites you to attend a seminar by Dr. Suleyman Ulusoy from Department of Mathematics and Natural Sciences, American University of Ras Al Khaimah, UAE.
Abstract: The first part of the talk will investigate a Keller-Segel model with quorum sensing and a fractional diffusion operator. This model describes the collective cell movement due to chemical sensing with flux limitation for high cell densities and with anomalous media represented by a nonlinear, degenerate fractional diffusion operator. The purpose is to introduce and prove the existence of a properly defined entropy solution. The second part of the talk will analyze an equation that is gradient flow of a functional related to Hardy-Littlewood-Sobolev inequality in whole Euclidean space R^d, d \geq 3. Under the hypothesis of integrable initial data with finite second moment and energy, we show local-in-time existence for any mass of "free-energy solutions", namely weak solutions with some free energy estimates. We exhibit that the qualitative behavior of solutions is decided by a critical value. The motivation for this part is to generalize Keller-Segel model to higher dimensions.
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