Speaker: Shengquan Xiang is an Assistant Professor at Peking University. He received his Ph.D. from Sorbonne University under the supervision of Prof. Jean-Michel Coron, and his bachelor degree from Peking University. His research interests focus on the control and related problems of partial differential equations.

Date: October 17, 2024

Time: 11:00-12:00 am

Location: B924, Zhixin Building, Shandong University

Sponsor: School of Mathematics, Shandong University

Abstract:

Recently, together with Coron and Krieger, we initiated a topic on the global control of geometric equations, first on wave map equations and then on the harmonic map heat flow. Combining ideas from control theory heat flow, differential geometry, and asymptotic analysis, we obtain several important properties, such as small-time local controllability, local quantitative rapid stabilization, obstruction to semi-global asymptotic stabilization, and global controllability to geodesics. Surprisingly, due to the geometric feature of the equation we also discover the small-time global controllability between harmonic maps within the same homotopy class for general compact Riemannian manifold targets, which is to be compared with the analogous but longstanding problem for the nonlinear heat equations.

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