À propos de certains problèmes inverses hybrides

Giovanni S. Alberti[1]; Yves Capdeboscq[1]

  • [1] Mathematical Institute Andrew Wiles Building Radcliffe Observatory Quarter Woodstock Road, Oxford OX2 6GG United Kingdom

Séminaire Laurent Schwartz — EDP et applications (2013-2014)

  • page 1-9
  • ISSN: 2266-0607

Abstract

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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.

How to cite

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Alberti, Giovanni S., and Capdeboscq, Yves. "À propos de certains problèmes inverses hybrides." Séminaire Laurent Schwartz — EDP et applications (2013-2014): 1-9. <http://eudml.org/doc/275679>.

@article{Alberti2013-2014,
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.},
affiliation = {Mathematical Institute Andrew Wiles Building Radcliffe Observatory Quarter Woodstock Road, Oxford OX2 6GG United Kingdom; Mathematical Institute Andrew Wiles Building Radcliffe Observatory Quarter Woodstock Road, Oxford OX2 6GG United Kingdom},
author = {Alberti, Giovanni S., Capdeboscq, Yves},
journal = {Séminaire Laurent Schwartz — EDP et applications},
language = {fre},
pages = {1-9},
publisher = {Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique},
title = {À propos de certains problèmes inverses hybrides},
url = {http://eudml.org/doc/275679},
year = {2013-2014},
}

TY - JOUR
AU - Alberti, Giovanni S.
AU - Capdeboscq, Yves
TI - À propos de certains problèmes inverses hybrides
JO - Séminaire Laurent Schwartz — EDP et applications
PY - 2013-2014
PB - Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique
SP - 1
EP - 9
AB - 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.
LA - fre
UR - http://eudml.org/doc/275679
ER -

References

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  1. G. S. Alberti. On multiple frequency power density measurements. Inverse Problems, 29(11) :115007, 25, 2013. Zbl1288.35204MR3116343
  2. G. S. Alberti. On multiple frequency power density measurements II. The full Maxwell’s equations. submitted, 2013. MR3116343
  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. Zbl0723.35082MR1147209
  5. G. Alessandrini and V. Nesi. Univalent σ -harmonic mappings. Arch. Rat. Mech. Anal., 158 :155–171, 2001. Zbl0977.31006MR1838656
  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. Zbl1167.35541MR2557649
  7. H. Ammari. An introduction to mathematics of emerging biomedical imaging, volume 62 of Mathématiques & Applications (Berlin). Springer, Berlin, 2008. Zbl1181.92052MR2440857
  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. Zbl1156.35101MR2424952
  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. Zbl1257.74091MR2736968
  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. Zbl1262.65204MR3022218
  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. Zbl1235.31006MR2873260
  12. Habib Ammari, Laure Giovangigli, Loc Hoang Nguyen, and Jin-Keun Seo. Admittivity imaging from multi-frequency micro-electrical impedance tomography. http://arxiv.org/abs/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. Zbl1111.35004MR2195135
  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. Zbl1267.35249MR3063538
  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. Zbl1330.35121MR1871388
  16. M. Briane. Isotropic realizability of electric fields around critical points. Discrete and Continuous Dynamical Systems - Series B, 19 :353–372, 2014. Zbl1286.35071MR3170189
  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. Zbl1118.78009MR2073507
  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. Zbl1315.35021MR3177847
  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. MR590275
  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. Zbl1180.35549MR2559157
  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. Zbl1259.92065MR2885203
  22. R. S. Laugesen. Injectivity can fail for higher-dimensional harmonic extensions. Complex Variables Theory Appl., 28(4) :357–369, 1996. Zbl0871.54020MR1700199
  23. N. Mandache. Exponential instability in an inverse problem for the Schrödinger equation. Inverse Problems, 17(5) :1435, 2001. Zbl0985.35110MR1862200
  24. Antonios D. Melas. An example of a harmonic map between Euclidean balls. Proc. Amer. Math. Soc., 117(3) :857–859, 1993. Zbl0836.54007MR1112497
  25. Siegfried Momm. Lower bounds for the modulus of analytic functions. Bull. London Math. Soc., 22(3) :239–244, 1990. Zbl0668.30001MR1041137
  26. G. Uhlmann. Electrical impedance tomography and Calderón’s problem. Inverse Problems, 25(12) :123011, 2009. Zbl1181.35339
  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. Zbl1259.78035

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