报告题目：Normalized solutions and limit profiles of the Gross-Pitaevskii-Poisson equation

报告摘要：Gross-Pitaevskii-Poisson (GPP) equation is a nonlocal modification of the Gross-Pitaevskii equation with an attractive Coulomb-like term. It appears in the models of self-gravitating Bose-Einstein condensates proposed in cosmology and astrophysics to describe Cold Dark Matter and Boson Stars. We investigate the existence of prescribed mass (normalised) solutions to the GPP equation, paying special attention to the shape and asymptotic behaviour of the associated mass-energy relation curves and to the limit profiles of solutions at the endpoints of these curves. In particular, we show that after appropriate rescalings, the constructed normalized solutions converge either to a ground state of the Choquard equation, or to a compactly supported radial ground state of the integral Thomas-Fermi equation. In different regimes the constructed solutions include global minima, local but not global minima and unstable mountain-pass type solutions. This is a joint work with Riccardo Molle (Rome Tor Vergata) and Giuseppe Riey (Calabria).

报告人简介：维塔利・莫罗兹是国际非局部偏微分方程领域知名学者，曾任斯旺西大学数学系主任（2021—2024）。研究方向覆盖托马斯 - 费米模型、石墨烯数学分析、玻色 - 爱因斯坦凝聚相关偏微分方程。最具代表性的学术贡献是重启并极大推动了乔夸尔方程的理论发展，多篇成果入选数学领域高被引论文。担任《伦敦数学会杂志》《爱丁堡皇家学会会刊 A 辑》等多个顶级数学期刊编委，长期主持英国利华休姆信托基金科研项目。

报告时间：2026年7月21日 10:30-11:30

报告地点：武之楼412教室