学术活动

Nonlinear aggregation-diffusion equations:(reverse) HLS inequalities and equilibration - Professor Jose. A. Carrillo(Imperial College London)

作者:   来源:  时间:2019-08-17

题目: Nonlinear aggregation-diffusion equations:(reverse) HLS inequalities and equilibration

报告人:Professor Jose. A. Carrillo
          (Imperial College London)

Abstract:  We analyse under which conditions equilibration between two competing effects, repulsion modelled by nonlinear diffusion and attraction modelled by nonlocal interaction, occurs. I will discuss the regimes that appear in aggregation diffusion problems with homogeneous kernels. We will discuss the main qualitative properties in terms of stationary states and minimizers of the free energies. In particular, all the porous medium cases are critical while the fast diffusion are not in this regime. In the second part, I will discuss the diffusion dominated case for porous medium cases in which this balance leads to continuous compactly supported radially decreasing equilibrium configurations for all masses. All stationary states with suitable regularity are shown to be radially symmetric by means of continuous Steiner symmetrisation techniques. Calculus of variations tools allow us to show the existence of global minimizers among these equilibria. Finally, in the fast diffusion regime we are able to find conditions for the existence of global minimizers in a different range by means of reverse HLS inequalities. Concentration at the origin in part of this range is not ruled out. This talk is based on works in collaboration with S. Hittmeir, B. Volzone, and Y. Yao (to appear in Inventiones Mathematicae), with V. Calvez and F. Hoffmann (Nonlinear Analisys TMA), and with J. Dolbeault, M. Delgadino, F. Hoffmann and R. Frank (to appear in J. Math. Pure Appl.).

时间:2019年8月17日(周六)下午15:00-16:00

地点:首都师范大学本部教二楼 527 教室

联系人:李海梁

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