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All issues Volume 52 / No 1 (January–February 2018) ESAIM: M2AN, 52 1 (2018) 123-145 References
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Issue
ESAIM: M2AN
Volume 52, Number 1, January–February 2018
Page(s) 123 - 145
DOI https://doi.org/10.1051/m2an/2018008
Published online 04 May 2018
  1. V. Baronian, L. Bourgeois and A. Recoquillay, Imaging an acoustic waveguide from surface data in the time domain. Wave Motion 66 (2016) 68–87. [Google Scholar]
  2. E. Bécache, L. Bourgeois, L. Franceschini and J. Dardé, Application of mixed formulations of quasi-reversibility to solve ill-posed problems for heat and wave equations: the 1D case. Inverse Probl. Imaging 9 (2015) 971–1002. [CrossRef] [Google Scholar]
  3. F.B. Belgacem, Why is the Cauchy problem severely ill-posed? Inverse Probl. 23 (2007) 823–836. [Google Scholar]
  4. L. Bourgeois, A mixed formulation of quasi-reversibility to solve the Cauchy problem for Laplace’s equation. Inverse Probl. 21 (2005) 1087–1104. [Google Scholar]
  5. L. Bourgeois and J. Dardé, A quasi-reversibility approach to solve the inverse obstacle problem. Inverse Probl. Imaging 4 (2010) 351–377. [CrossRef] [Google Scholar]
  6. L. Bourgeois and J. Dardé, The “exterior approach” to solve the inverse obstacle problem for the Stokes system. Inverse Probl. Imaging 8 (2014) 23–51. [CrossRef] [Google Scholar]
  7. L. Bourgeois and J. Dardé, The “exterior approach” applied to the inverse obstacle problem for the heat equation. SIAM J. Numer. Anal. 55 (2017) 1820–1842. [Google Scholar]
  8. L. Bourgeois and E. Lunéville, The linear sampling method in a waveguide: a modal formulation. Inverse Probl. 24 (2008) 015018. [Google Scholar]
  9. L. Bourgeois, C. Chambeyron and S. Kusiak, Locating an obstacle in a 3d finite depth ocean using the convex scattering support. Special Issue: The Seventh International Conference on Mathematical and Numerical Aspects of Waves (WAVES05). J. Comput. Appl. Math. 204 (2007) 387–399. [Google Scholar]
  10. F. Brezzi and M. Fortin, Mixed and Hybrid Finite Element Methods. Vol. 15 of Springer Series in Computational Mathematics. Springer-Verlag, New York (1991). [CrossRef] [Google Scholar]
  11. M. Burger and S. J. Osher, A survey on level set methods for inverse problems and optimal design. Eur. J. Appl. Math. 16 (2005) 263–301. [Google Scholar]
  12. E. Burman, Stabilized finite element methods for nonsymmetric, noncoercive, and ill-posed problems. Part I: Elliptic equations. SIAM J. Sci. Comput. 35 (2013) A2752–A2780. [Google Scholar]
  13. E. Burman, The elliptic Cauchy problem revisited: control of boundary data in natural norms. C. R. Math. Acad. Sci. Paris 355 (2017) 479–484. [CrossRef] [Google Scholar]
  14. E. Burman, A stabilized nonconforming finite element method for the elliptic Cauchy problem. Math. Comp. 86 (2017) 75–96. [CrossRef] [Google Scholar]
  15. A. Charalambopoulos, D. Gintides, K. Kiriaki and A. Kirsch, The factorization method for an acoustic wave guide, in Mathematical Methods in Scattering Theory and Biomedical Engineering. World Sci. Publ., Hackensack, NJ (2006) 120–127. [CrossRef] [Google Scholar]
  16. N. Cîndea and A. Münch, Inverse problems for linear hyperbolic equations using mixed formulations. Inverse Probl. 31 (2015) 075001. [Google Scholar]
  17. C. Clason and M. V. Klibanov, The quasi-reversibility method for thermoacoustic tomography in a heterogeneous medium. SIAM J. Sci. Comput. 30 (2007/08) 1–23. [Google Scholar]
  18. J. Dardé, Iterated quasi-reversibility method applied to elliptic and parabolic data completion problems. Inverse Probl. Imaging 10 (2016) 379–407. [CrossRef] [Google Scholar]
  19. J. Dardé, A. Hannukainen and N. Hyvönen, An Hdiv-based mixed quasi-reversibility method for solving elliptic Cauchy problems. SIAM J. Numer. Anal. 51 (2013) 2123–2148. [Google Scholar]
  20. A. Ern and J.-L. Guermond, in Theory and Practice of Finite Elements. Vol. 159 of Applied Mathematical Sciences. Springer-Verlag, New York (2004). [CrossRef] [Google Scholar]
  21. A. Henrot and M. Pierre, in Variation et optimisation de formes: une analyse géométrique. [A geometric analysis]. Vol. 48 of Mathématiques & Applications (Berlin) [Mathematics & Applications]. Springer, Berlin (2005). [Google Scholar]
  22. V. Isakov, in Inverse Problems for Partial Differential Equations. Vol. 127 of Applied Mathematical Sciences, second edn. Springer, New York (2006). [Google Scholar]
  23. K. Ito and B. Jin, Inverse Problems: Tikhonov Theory and Algorithms. Vol. 22 of Series on Applied Mathematics. World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ (2015). [Google Scholar]
  24. A. Kirsch, in An Introduction to the Mathematical Theory of Inverse Problems. Vol. 120 Applied Mathematical Sciences. Springer-Verlag, New York (1996). [CrossRef] [Google Scholar]
  25. M.V. Klibanov and F. Santosa, A computational quasi-reversibility method for Cauchy problems for Laplace’s equation. SIAM J. Appl. Math. 51 (1991) 1653–1675. [Google Scholar]
  26. R. Lattès and J.-L. Lions, Méthode de quasi-réversibilité et applications, in Travaux et Recherches Mathématiques. No. 15, Dunod, Paris (1967). [Google Scholar]
  27. K. Liu, Y. Xu and J. Zou, Imaging wave-penetrable objects in a finite depth ocean. Appl. Math. Comput. 235 (2014) 364–376. [Google Scholar]
  28. W. McLean, Strongly Elliptic Systems and Boundary Integral Equations. Cambridge University Press, Cambridge (2000). [Google Scholar]
  29. P. Monk and V. Selgas, An inverse acoustic waveguide problem in the time domain. Inverse Probl. 32 (2016) 055001. [Google Scholar]
  30. P. Stefanov and G. Uhlmann, Local uniqueness for the fixed energy fixed angle inverse problem in obstacle scattering. Proc. Am. Math. Soc. 132 (2004) 1351–1354. [Google Scholar]

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