Radiation conditions for wave in stratified medium and related inverse scattering problems
Speaker:Prof. Yongzhi Steve Xu
Professor
Department of Mathematics
University of Louisville
Date & Time:23 Jul 2010 (Friday) 16:00 - 17:00
Venue:L108
Organized by:Department of Mathematics

Abstract

Waves from a point source in a homogeneous medium will propagate spherically. This can be described by the Sommerfeld radiation condition. However, it is hard to use simple formula to describe radiation conditions for wave propagation in a stratified medium. A generalized Sommerfeld radiation was proposed by Xu in 1990, applying contour integral and asymptotic approximation. The study in this area becomes more active recently. Papers in 2009 and 2010 from different aspects presented regorous analysis for results similar to Xu's condition.

On the other hand, Chandler-Wolde and his coworkers introduced the upward propagating radiation condition for wave in essentially homogeneous medium with rough boundary.

This talk will discuss the radiation conditions, and introduce an upward propagating radiation condition and a sideward radiation condition for waves in essentially layered medium.

Some related inverse scattering problems will be discussed.

Biography

Dr. Yongzhi Steve Xu is currently a Professor in the Department of Mathematics, University of Louisville. He is also member of editorial boards of the following:

  • Co-Editor in Chief of Applicable Analysis
  • Mathematical Methods in Applied Sciences
  • Complex Variables and Elliptic Equations