偏微分方程+数值计算+控制论 学术报告

Title: Waves in non smooth and discrete media

Speaker: Enrique Zuazua (BCAM – Basque Center for Applied Mathematics)

Host: Chuang Zheng

Time: 16:00-17:00, August 9, 2015

Room: 1220 Main Building

 

ABSTRACT

 

We shall discuss several problems, motivated by control theoretical issues and inverse problems, related with wave propagation in non smooth media.

 

When waves propagate in smooth media, the evolution of energy can be understood along rays of Geometric Optics. But, as we shall see, in rough media, waves can get trapped in the interior of the domain where they evolve, never reaching the boundary. This makes boundary observation and control impossible.

 

This phenomenon  is due to the existence of concentrated quasi-modes and gaussian beams that are also an impediment for dispersive properties to hold.

 

We shall also discuss closely related issues emerging in the context of numerical approximation, describing how the geometry of the mesh may affect propagation properties of numerical solutions.

额外信息