Abstract: We discuss 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 characterization of the limit profiles of the groundstates when perturbation parameter is small. We also outline the behaviour of groundstates when perturbation is strong. In some of the regimes the limit profile is given by a compactly supported discontinuous minimizer of a Thomas-Fermi type variational problem. This is joint work with Zeng Liu (Suzhou, China) and Damiano Greco (Swansea).

嘉宾简介：Vitaly Moroz教授，Swansea大学数学系主任。Moroz教授的研究方向主要为偏微分方程，尤其是具有非局部作用的非线性方程，包括模拟不同尺度的自交互多体系统的集体行为，从原子和分子到动物群和社会群体中的群体模式，直至黑洞和星系的形成。特别地，他与Jean Van Schaftingen教授的一系列合作工作对Choquard 方程理论的发展起到重要推动作用，其中5篇文章被Web of Science列为Highly Cited Papers in Mathematics。