June 18,  19,  20   2003
 
 
 

02:30 PM - Friday, June 20, 2003 - Amphitheater Hermite

Masahiro Yamamoto

Department of Mathematical Sciences
University of Tokyo
3-8-1 Komaba, Tokyo 153-8914, Japan

myama@ms.u-tokyo.ac.jp

Uniqueness in Determining Coefficients in Maxwell's Equations and Lamé Equation

We consider non-stationary isotropic Maxwell's equations and Lamé equations wherephysical coefficients are depending on spatial variables (but not on the time variable). We discuss inverse problems of determining such coefficients from overdetermining data on side boundary (i.e., on a suitable boundary of the spatial domain over a finite time interval). We will choose a finite number of suitable initial data to take boundary observations. We establish (1) conditional stability in determining the permittivity and the permeability for Maxwell's equations (2) conditional stability in determning density and two Lamé coefficients for the Lamé equation with the minimum number of initial data (especially for (2) a single choice of suitable initial data is sufficient). The technique is based on Carleman estimates in Sobolev spaces of negative orders.