Mathematical foundations of the time reversal mirror

Article type: Research Article

Authors: Bardos, Claude | Fink, Mathias

Affiliations: University Denis Diderot, LAN (University Pierre et Marie Curie) and CMLA ENS‐Cachan, France E‐mail: bardos@math.jussieu.fr | Laboratoire Ondes et Acoustique, ESPCI, Université Denis Diderot, UMR CNRS 7587, 10, rue Vauquelin, 75005 Paris, France E‐mail: mathias.fink@espci.fr

Abstract: In the present paper a mathematical analysis of the “time reversal mirror” (cf. [4,9,10]) is given. As a first step of a more detailed program, the emphasis is put on phenomena which are described by the genuine acoustic equation with Dirichlet or “impedance” boundary conditions. An ideal situation is first considered then relation between the question of the local decay of energy and the accuracy of the method are exploited. The positive effect of the ergodicity is explained and eventually comparison with control theory approach is considered.

Journal: Asymptotic Analysis, vol. 29, no. 2, pp. 157-182, 2002