Tsinghua-BIMSA Analysis&PDE Seminar

主讲人 Speaker: Mengxuan Yang
时间 Time: Fri.  10:00-11:00,2021 - 11 - 5 ~ 12 - 31
地点 Venue:腾讯会议

摘要 Abstract

Title: Diffraction and Wave Trace of the Aharonov--Bohm Hamiltonian
Speaker: Mengxuan Yang(Northwestern University)
Time: Fri. 10:00-11:00 am, Nov. 5, 2021
腾讯会议ID: 316 6279 6976, 密码:370371

Abstract: Hormander's classic theorem shows that singularities of solutions to the wave equation propagate along the geodesic flow. Duistermaat--Guillemin trace formula gives leading order singularities of the wave trace on closed manifolds. In this talk, we will discuss the analogous results for wave equations with singular magnetic vector potentials, which correspond to the celebrated Aharonov--Bohm effect. A result on a lower bound of the number of resonances will also be discussed. 

Title: Boundary Stabilisation of Waves on Product Manifolds

Speaker: Ruoyu P. T. Wang (Northwestern University)
Time: Fri. 10:00-11:00 am, Nov. 12, 2021
腾讯会议ID: 316 6279 6976, 密码:370371
Abstract: Take a square and consider the damped waves with boundary damping $a>0$ on the top side only. This system models the acoustic waves in a square domain, where the top side is made of dissipative materials leading to the loss of energy whenever the waves interact with the top side. We will discuss my recent result implying that the energy of those waves must uniformly decay no faster than $t^{-1/2}$, and no slower than it. We will also discuss this result in the context of product manifolds where the transverse geometric control is sufficient but not necessary for such energy decay.