学术报告报告主题: Critical Mass Phenomena of Ground States in Stationary Second Order Mean-field Games Systems
报 告 人: 曾小雨
报告时间： 2024年 12月6日（星期五）下午14:00-15:00
报告地点： 腾讯会议：229-675-078
邀 请 人: 王友军 副教授
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数学学院
2024年12月6日
报告摘要:
Mean-field games (MFG) systems serve as paradigms to qualitatively describe the game among a huge number of rational players. In this talk, some intricate connections between MFGs and Schrodinger equations are mentioned, then the existence and asymptotic profiles of ground states to MFG systems in the mass critical exponent case are extensively discussed. First of all, we establish the optimal Gagliardo-Nirenberg type inequality associated with the potential-free MFG system. Then, under some mild assumptions on the potential function, we show that there exists a critical mass M* such that the MFG system admits a least energy solution if and only if the total mass of population density M is less than M*. Moreover, the blow-up behavior of energy minimizers are captured as M increases and converges to M*. In particular, given the precise asymptotic expansions of the potential, we establish the refined blow-up behavior of ground states. While studying the existence of least energy solutions, we analyze the maximal regularities of solutions to Hamilton-Jacobi equations with superlinear gradient terms. This is a joint work with Marco Cirant, Fanze Kong and Juncheng Wei.
报告人介绍：
曾小雨，武汉理工大学教授，2009年本科毕业于华中师范大学，2014年博士毕业于中科院武汉物理与数学研究所。研究方向为非线性泛函分析及椭圆型偏微分方程，主要从事与薛定谔方程以及玻色-爱因斯坦凝聚相关的变分问题研究。主持国家自然科学基金面上项目和青年科学基金项目，优秀青年科学基金获得者,并作为核心成员参与国家自然科学基金重点项目。主要成果发表在Trans.AMS、JFA、Ann. Inst. H. Poincar'eAnal. Non Lin'eaire、Nolinearity、J. Differential Equations等国际期刊上。