PDE and Applied Mathematics Seminar
February 19 (Crouse Hall 210, 2:30-3:30 pm) Ihsan Topaloglu (McMaster University, Canada) will speak on "Minimizers of Purely Nonlocal Attractive-Repulsive Energies via Interaction Regularization".
Purely nonlocal attractive-repulsive energies have attracted quite some interest in the recent years. The asymptotic states of many physical and biological systems such as in models of granular media, molecular self-assembly, biological swarming and collective behavior of many-agent systems can be described as minimizers of such energies. In this talk we consider minimizers of a purely nonlocal energy defined via a pairwise singular interaction kernel given in the power-law form. Inspired by the so-called vortex blob methods and the numerical studies on the nonlocal aggregation equation related to the energy under consideration we look at the regularization of this nonlocal energy by convoluting the interaction kernel with mollifiers. We then prove Gamma-convergence of regularized energies in the space of probability measures with finite second moment endowed with the 2-Wasserstein metric, and obtain the convergence of minimizers after establishing a compactness result. Finally, we prove the convergence of gradient flows of these regularized energies for quadratic attraction and Coulomb repulsion. This is a joint work with Katy Craig.
April 2 and 9 (CAS 220, 2:00-3:30 pm) Fedor Nazarov (Kent State University) will speak on "
The mass kinetics and the persistence problem".
April 16 (CAS 220, 2:00-3:00 pm) Vitaly Moroz (Swansea University, UK) will speak on "Ground-states of a Schrodinger-Poisson-Slater type equation".
Schrodinger-Poisson-Slater equation is a nonlinear modification of Schrodinger equation
with a repulsive nonlocal Coulomb potential and a local nonlinearity.
We develop a variational framework for a class of Schrodinger-Poisson-Slater type equations
and discuss existence, positivity and radial symmetry of ground-state solutions.
This is a joint work with Carlo Mercuri (Swansea) and Jean Van Schaftingen (Louvain-la-Neuve).