报告题目：Asymptotic profiles of groundstates for a class of Choquard equations
报告人：Vitaly Moroz 教授（英国斯旺西大学）
摘要：We study the asymptotic behaviour of groundstates for a class of singularly perturbed Choquard type equations with a local repulsion term. We identify seven different asymptotic regimes and provide a characterisation of the limit profiles of the groundstates when perturbation parameter is small. We also outline the behaviour of groundstates when perturbation is strong. This is joint work with Zeng Liu (Suzhou, China).
报告人简介：Vitaly Moroz is a Professor at Mathematics Department, Swansea University. His research is in the Analysis of Nonlinear Partial Differential Equations (PDEs). It is focussed on the fundamental questions of existence, non-existence, and structure of solution sets of nonlinear elliptic equations and inequalities. Recently he was mostly working on nonlinear Schrödinger type equations with nonlocal interactions, such as Choquard-Pekar (Schrödinger-Newton) equations, Schrödinger-Poisson type equations, nonlocal Hartree type equations arising in the density functional theory models for graphene. The common mathematical feature of all these models is that, unlike in the case of classical local PDEs, nonlocal terms are present in the equations via Coulombian type interactions or via a fractional Laplacian term, or both. The tools employed are from the Calculus of Variations, elliptic PDEs theory and Potential Theory.