报告题目：Critical Mass Phenomena and Blow-up Behaviors of Ground States in Stationary Second Order Mean-field Games Systems with Decreasing Cost

报告人：孔繁泽 博士 （加拿大不列颠哥伦比亚大学）

报告时间：2024年5月15日 上午9:00-12:00

腾讯会议ID：127-511-691

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, Juncheng Wei and Xiaoyu Zeng.

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主讲人简介：孔繁泽，加拿大不列颠哥伦比亚大学博士，研究方向为反应扩散方程、平均场博弈方程解的集中现象。近年来在SIAM J. Math. Anal.、Math. Models Methods Appl. Sci.、Journal of Nonlinear Sciences、JDE等知名数学期刊上发表学术论文十多篇。