June 18,  19,  20   2003
 
 
 

04:30 PM - Wednesday, June 18, 2003 - Amphitheater Darboux

Benoît Perthame

DMA
Ecole Normale Supérieure
45, rue d'Ulm
75230 Paris Cedex 05 France

Benoit.Perthame@ens.fr

Helmholtz Equation in the Full Space: Estimate and Radiation Condition at Infinity

The Helmholtz Equations describes the wave propagation with a fixed frequency. It is used for a large range of applications like radars, underwater acoustics or sysmic waves. In several type of applications variable index (speed of propagations) are needed. We will first recall some results concerning the existence of solutions and a priori bounds for refraction indices satisfying weak dispersive assumptions. Then, we will derive a Sommerfeld condition at infinity for an index which is not constant at infinity. Its analysis relies on a new estimate for the decay of energy at infinity that uses specifically the index gradient.