Center for diffusion of mathematic journals

 
 
 
 

Séminaire Laurent Schwartz — EDP et applications

Table of contents for this volume | Previous article | Next article
Giovanni S. Alberti; Yves Capdeboscq
À propos de certains problèmes inverses hybrides
Séminaire Laurent Schwartz — EDP et applications (2013-2014), Exp. No. 2, 9 p., doi: 10.5802/slsedp.50
Article PDF

Résumé - Abstract

Dans cet exposé, nous présentons quelques résultats récents concernant certains problèmes d’identification de paramètres de type hybride, aussi appelés multi-physiques, pour lesquels le modèles physique sous-jacent est une équation aux dérivées partielles elliptique.

Bibliography

[1] G. S. Alberti. On multiple frequency power density measurements. Inverse Problems, 29(11) :115007, 25, 2013.  MR 3116343 |  Zbl pre06277373
[2] G. S. Alberti. On multiple frequency power density measurements II. The full Maxwell’s equations. submitted, 2013.  MR 3116343
[3] G. S. Alberti. Enforcing local non-zero-constraints in pde and applications to hybrid imaging problems. sub, page 23, 2014.
[4] G. Alessandrini. Determining conductivity by boundary measurements, the stability issue. In Renato Spigler, editor, Applied and Industrial Mathematics, volume 56 of Mathematics and Its Applications, pages 317–324. Springer Netherlands, 1991.  MR 1147209 |  Zbl 0723.35082
[5] G. Alessandrini and V. Nesi. Univalent $\sigma $-harmonic mappings. Arch. Rat. Mech. Anal., 158 :155–171, 2001.  MR 1838656 |  Zbl 0977.31006
[6] Giovanni Alessandrini, Antonino Morassi, Edi Rosset, and Sergio Vessella. On doubling inequalities for elliptic systems. J. Math. Anal. Appl., 357(2) :349–355, 2009.  MR 2557649 |  Zbl 1167.35541
[7] H. Ammari. An introduction to mathematics of emerging biomedical imaging, volume 62 of Mathématiques & Applications (Berlin). Springer, Berlin, 2008.  MR 2440857 |  Zbl 1181.92052
[8] H. Ammari, E. Bonnetier, Y. Capdeboscq, M. Tanter, and M. Fink. Electrical impedance tomography by elastic deformation. SIAM J. Appl. Math., 68(6) :1557–1573, 2008.  MR 2424952 |  Zbl 1156.35101
[9] H. Ammari, E. Bossy, V. Jugnon, and H. Kang. Mathematical modeling in photoacoustic imaging of small absorbers. SIAM Rev., 52(4) :677–695, 2010.  MR 2736968 |  Zbl 1257.74091
[10] H. Ammari, E. Bretin, J. Garnier, and V. Jugnon. Coherent interferometry algorithms for photoacoustic imaging. SIAM J. Numer. Anal., 50(5) :2259–2280, 2012.  MR 3022218 |  Zbl 1262.65204
[11] H. Ammari, Y. Capdeboscq, F. de Gournay, A. Rozanova-Pierrat, and F. Triki. Microwave imaging by elastic deformation. SIAM J. Appl. Math., 71(6) :2112–2130, 2011.  MR 2873260 |  Zbl 1235.31006
[12] Habib Ammari, Laure Giovangigli, Loc Hoang Nguyen, and Jin-Keun Seo. Admittivity imaging from multi-frequency micro-electrical impedance tomography. arXiv :1403.5708, 2014.
[13] K. Astala and L. Päivärinta. Calderón’s inverse conductivity problem in the plane. Ann. of Math. (2), 163(1) :265–299, 2006.  MR 2195135 |  Zbl 1111.35004
[14] G. Bal, E. Bonnetier, F. Monard, and F. Triki. Inverse diffusion from knowledge of power densities. Inverse Probl. Imaging, 7(2) :353–375, 2013.  MR 3063538 |  Zbl 1267.35249
[15] Patricia Bauman, Antonella Marini, and Vincenzo Nesi. Univalent solutions of an elliptic system of partial differential equations arising in homogenization. Indiana Univ. Math. J., 50(2) :747–757, 2001.  MR 1871388 |  Zbl pre01780879
[16] M. Briane. Isotropic realizability of electric fields around critical points. Discrete and Continuous Dynamical Systems - Series B, 19 :353–372, 2014.  MR 3170189 |  Zbl pre06266120
[17] M. Briane, G. W. Milton, and V. Nesi. Change of sign of the corrector’s determinant for homogenization in three-dimensional conductivity. Arch. Ration. Mech. Anal., 173(1) :133–150, 2004.  MR 2073507 |  Zbl 1118.78009
[18] M. Briane, G. W. Milton, and A. Treibergs. Which electric fields are realizable in conducting materials ? ESAIM : Mathematical Modelling and Numerical Analysis, 48 :307–323, 3 2014.  MR 3177847
[19] A.-P. Calderón. On an inverse boundary value problem. In Seminar on Numerical Analysis and its Applications to Continuum Physics (Rio de Janeiro, 1980), pages 65–73. Soc. Brasil. Mat., Rio de Janeiro, 1980.  MR 590275
[20] Y. Capdeboscq, J. Fehrenbach, F. de Gournay, and O. Kavian. Imaging by modification : numerical reconstruction of local conductivities from corresponding power density measurements. SIAM J. Imaging Sci., 2(4) :1003–1030, 2009.  MR 2559157 |  Zbl 1180.35549
[21] P. Kuchment and L. Kunyansky. Mathematics of photoacoustic and thermoacoustic tomography. In Otmar Scherzer, editor, Handbook of Mathematical Methods in Imaging, pages 817–865. Springer New York, 2011.  MR 2885203 |  Zbl 1259.92065
[22] R. S. Laugesen. Injectivity can fail for higher-dimensional harmonic extensions. Complex Variables Theory Appl., 28(4) :357–369, 1996.  MR 1700199 |  Zbl 0871.54020
[23] N. Mandache. Exponential instability in an inverse problem for the Schrödinger equation. Inverse Problems, 17(5) :1435, 2001.  MR 1862200 |  Zbl 0985.35110
[24] Antonios D. Melas. An example of a harmonic map between Euclidean balls. Proc. Amer. Math. Soc., 117(3) :857–859, 1993.  MR 1112497 |  Zbl 0836.54007
[25] Siegfried Momm. Lower bounds for the modulus of analytic functions. Bull. London Math. Soc., 22(3) :239–244, 1990.  MR 1041137 |  Zbl 0668.30001
[26] G. Uhlmann. Electrical impedance tomography and Calderón’s problem. Inverse Problems, 25(12) :123011, 2009.  Zbl 1181.35339
[27] K. Wang and M. A. Anastasio. Photoacoustic and thermoacoustic tomography : Image formation principles. In O. Scherzer, editor, Handbook of Mathematical Methods in Imaging, pages 781–815. Springer New York, 2011.  Zbl 1259.78035
Copyright Cellule MathDoc 2019 | Credit | Site Map