报告人:吴丽江博士 (美国卡内基梅隆大学)
报告题目:NONLOCAL INTERACTION EQUATIONS ON MANIFOLDS WITH BOUNDARY
报告时间:2013年12月27日(星期五)10:30
报告地点:数学实验室
Abstract: In this presentation, we discuss biological aggregation in a heterogeneous environment by modeling the environment as a Riemannian manifold with boundary. We develop gradient flow approach in the space of probability measures on the manifold endowed with Riemannian 2-Wasserstein metric. Wethen show the existence and stability of weak measure solutions to a class of nonlocal interaction equationsthrough the existence of gradient flows. We discuss how heterogeneity of the environment leads to newdynamical phenomena. In particular exposed to a unidirectional external potential the agents form a rollingtravelling wave (in contrast to the translational motion in the homogeneous environment). We close the presentation by giving some simulations to show the rolling phenomenon.
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