Le but de cette note est d'introduire les conditions absorbantes retournées temporellement (TRAC) dans les méthodes de retournement temporel. Elles rendent possible la « reconstruction du passé » sans connaître la source émettrice des signaux enregistrés puis rétropropagés. Cette nouvelle méthode ne nécessite pas de connaissance a priori des propriétés physiques de l'inclusion. Nous démontrons une estimation d'énergie pour le problème non standard obtenu. Deux applications aux problèmes inverses sont proposées.
The aim of this note is to introduce the time reversed absorbing conditions (TRAC) in time reversal methods. These new boundary conditions enable one to “recreate the past” without knowing the source which has emitted the signals that are back-propagated. This new method does not rely on any a priori knowledge of the physical properties of the inclusion. We prove an energy estimate for the resulting non-standard boundary value problem. Two applications to inverse problems are given.
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@article{CRMATH_2010__348_19-20_1063_0, author = {Assous, Franck and Kray, Marie and Nataf, Fr\'ed\'eric and Turkel, Eli}, title = {Time reversed absorbing conditions}, journal = {Comptes Rendus. Math\'ematique}, pages = {1063--1067}, publisher = {Elsevier}, volume = {348}, number = {19-20}, year = {2010}, doi = {10.1016/j.crma.2010.09.014}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.crma.2010.09.014/} }
TY - JOUR AU - Assous, Franck AU - Kray, Marie AU - Nataf, Frédéric AU - Turkel, Eli TI - Time reversed absorbing conditions JO - Comptes Rendus. Mathématique PY - 2010 SP - 1063 EP - 1067 VL - 348 IS - 19-20 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2010.09.014/ DO - 10.1016/j.crma.2010.09.014 LA - en ID - CRMATH_2010__348_19-20_1063_0 ER -
%0 Journal Article %A Assous, Franck %A Kray, Marie %A Nataf, Frédéric %A Turkel, Eli %T Time reversed absorbing conditions %J Comptes Rendus. Mathématique %D 2010 %P 1063-1067 %V 348 %N 19-20 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.crma.2010.09.014/ %R 10.1016/j.crma.2010.09.014 %G en %F CRMATH_2010__348_19-20_1063_0
Assous, Franck; Kray, Marie; Nataf, Frédéric; Turkel, Eli. Time reversed absorbing conditions. Comptes Rendus. Mathématique, Tome 348 (2010) no. 19-20, pp. 1063-1067. doi : 10.1016/j.crma.2010.09.014. http://archive.numdam.org/articles/10.1016/j.crma.2010.09.014/
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☆ This work was supported by the French–Israeli Grant FIST-MATHS2.