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All issues Volume 27 (2021) Supplement ESAIM: COCV, 27 (2021) S27 References
Open Access
Issue
ESAIM: COCV
Volume 27, 2021
Regular articles published in advance of the transition of the journal to Subscribe to Open (S2O). Free supplement sponsored by the Fonds National pour la Science Ouverte
Article Number S27
Number of page(s) 34
DOI https://doi.org/10.1051/cocv/2020086
Published online 01 March 2021
  1. L. Baudouin, M. de Buhan and S. Ervedoza, Global Carleman estimates for waves and applications. Commun. Partial Differ. Equ. 38 (2013) 823–859. [Google Scholar]
  2. L. Baudouin, M. de Buhan and S. Ervedoza, Convergent algorithm based on Carleman estimates for the recovery of a potential in the wave equation. SIAM J. Numer. Anal. 55 (2017) 1578–1613. [Google Scholar]
  3. M. Boulakia, C. Grandmont and A. Osses, Some inverse stability results for the bistable reaction–diffusion equation using Carleman inequalities. C. R. Math. Acad. Sci. Paris 347 (2009) 619–622. [Google Scholar]
  4. P.N. Brown and V. Saad, Convergence theory of non linear Newton-Krylov algorithms. SIAM J. Optim. 4 (1994) 297–330. [Google Scholar]
  5. A.L. Bukhgeĭm and M.V. Klibanov, Uniqueness in the large of a class of multidimensional inverse problems. Dokl. Akad. Nauk SSSR 260 (1981) 269–272. [Google Scholar]
  6. S. Butterworth, On the theory of filter amplifiers. Wirel. Eng. 7 (1930) 536–541. [Google Scholar]
  7. N. Cîndea, E. Fernández-Cara and A. Münch, Numerical controllability of the wave equation through primal methods and Carleman estimates. ESAIM: COCV 19 (2013) 1076–1108. [CrossRef] [EDP Sciences] [Google Scholar]
  8. P. Colli Franzone, L.F. Pavarino and S. Scacchi, Mathematical cardiac electrophysiology. Vol. 13 of MS&A. Modeling, Simulation and Applications. Springer, Cham (2014). [Google Scholar]
  9. H. Egger, H.W. Engl and M.V. Klibanov, Global uniqueness and Hölder stability for recovering a nonlinear source term in a parabolic equation. Inverse Probl. 21 (2005) 271–290. [Google Scholar]
  10. L.C. Evans, Partial differential equations. Vol. 19 of Graduate Studies in Mathematics. American Mathematical Society, Providence, RI, second edition (2010). [CrossRef] [Google Scholar]
  11. E. Fernández-Cara, M. González-Burgos, S. Guerrero and J.-P. Puel, Exact controllability to the trajectories of the heat equation with Fourier boundary conditions: the semilinear case. ESAIM: COCV 12 (2006) 466–483. [CrossRef] [EDP Sciences] [Google Scholar]
  12. E. Fernández-Cara, A. Münch and D.A. Souza, On the numerical controllability of the two-dimensional heat, Stokes and Navier-Stokes equations. J. Sci. Comput. 70 (2017) 819–858. [Google Scholar]
  13. A.V. Fursikov and O.Yu. Imanuvilov, Controllability of evolution equations. Vol. 34 of Lecture Notes Series. Seoul National University, Research Institute of Mathematics, Global Analysis Research Center, Seoul (1996). [Google Scholar]
  14. L.F. Ho, Observabilité frontière de l’équation des ondes. C. R. Acad. Sci. Paris Sér. I Math. 302 (1986) 443–446. [Google Scholar]
  15. O.Y. Imanuvilov and M. Yamamoto, Lipschitz stability in inverse parabolic problems by the Carleman estimate. Inverse Prob. 14 (1998) 1229–1245. [Google Scholar]
  16. K. Ito and B. Jin, Inverse problems. Vol. 22 of Series on Applied Mathematics. World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ (2015). Tikhonov theory and algorithms. [Google Scholar]
  17. M.V. Klibanov, Global convexity in a three-dimensional inverse acoustic problem. SIAM J. Math. Anal. 28 (1997) 1371–1388. [Google Scholar]
  18. M.V. Klibanov, Carleman estimates for global uniqueness, stability and numerical methods for coefficient inverse problems. J. Inverse Ill-Posed Probl. 21 (2013) 477–560. [Google Scholar]
  19. M.V. Klibanov and V.G. Kamburg, Globally strictly convex cost functional for an inverse parabolic problem. Math. Methods Appl. Sci. 39 (2016) 930–940. [Google Scholar]
  20. M.V. Klibanov, A.E. Kolesov and D.-L. Nguyen, Convexification method for an inverse scattering problem and its performance for experimental backscatter data for buried targets. SIAM J. Imag. Sci. 12 (2019) 576–603. [Google Scholar]
  21. D.A. Knoll and D.E. Keyes, Jacobian-free Newton-Krylov methods: a survey of approaches and applications. J. Comput. Phys. 193 (2004) 357. [Google Scholar]
  22. T.T. Le and L.H. Nguyen, A convergent numerical method to recover the initial condition of nonlinear parabolic equations from lateral Cauchy data. preprint. [Google Scholar]
  23. J.-L. Lions, Contrôlabilité exacte, perturbations et stabilisation de systèmes distribués. Tome 1. Contrôlabilité exacte. [Exact controllability], With appendices by E. Zuazua, C. Bardos, G. Lebeau and J. Rauch. Vol. 8 of Recherches en Mathématiques Appliquées [Research in Applied Mathematics]. Masson, Paris (1988). [Google Scholar]
  24. J.L. Lions and E. Magenes, Non-homogeneous boundary value problems and applications. In Vol. 1. Springer Science & Business Media (2012). [Google Scholar]
  25. A. Savitzky and M. Golay, Smoothing and differentiation of data by simplified least squares procedures. Anal. Chem. 8 (1964) 1627–39. [Google Scholar]
  26. K. Schmitt and R. Thompson, Nonlinear analysis and differential equations: An introduction. Lecture Notes. University of Utah, Department of Mathematics (1998). [Google Scholar]
  27. M. Yamamoto, Carleman estimates for parabolic equations and applications. Inverse Problems 25 (2009) 123013. [Google Scholar]

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