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ЖУРНАЛЫ // Записки научных семинаров ПОМИ

Зап. научн. сем. ПОМИ, 2012, том 409, страницы 121–129 (Mi znsl5515)

Equations of the Boundary Control method for the inverse source problem
A. S. Mikhaylov, V. S. Mikhaylov

Литература

1. C. Alves, A. L. Silvestre, T. Takahashi, M. Tucsnak, “Solving inverse source problems using observability. Applications to the Euler–Bernoulli plate equation”, SIAM J. Control Optim., 48:3 (2009), 1632–1659  crossref  mathscinet  zmath  isi
2. S. A. Avdonin, A. S. Bulanova, “Boundary control approach to the spectral estimation problem. The case of multiple poles”, Math. Contr. Sign. Syst., 22:3 (2011), 245–265  crossref  mathscinet  zmath  isi  elib
3. S. A. Avdonin, A. S. Bulanova, D. Nicolsky, “Boundary control approach to the spectral estimation problem. The case of simple poles”, Sampling Theory in Signal and Image Processing, 8:3 (2009), 225–248  mathscinet  zmath
4. S. Avdonin, F. Gesztesy, K. A. Makarov, “Spectral estimation and inverse initial boundary value problems”, Inverse Probl. Imaging, 4:1 (2010), 1–9  crossref  mathscinet  zmath  isi  elib
5. S. Avdonin, S. Ivanov, Families of Exponentials, Cambridge University Press, Cambridge, 1995  mathscinet  zmath
6. S. Avdonin, V. Mikhaylov, “The boundary control approach to inverse spectral theory”, Inverse Problems, 26:4 (2010), 045009, 19 pp.  crossref  mathscinet  zmath  isi  elib
7. S. Avdonin, V. Mikhaylov, “Inverse source problem for the 1-D Schrödinger equation”, Zap. Nauchn. Semin. POMI, 393, 2011, 5–11  mathnet  mathscinet
8. S. Avdonin, V. Mikhaylov, K. Ramdani, Reconstructing the potential for the 1D Schrödinger equation from boundary measurements, submitted
9. L. Baudouin, J.-P. Puel, “Uniqueness and stability in an inverse problem for the Schrödinger equation”, Inverse Problems, 18:6 (2002), 1537–1554  crossref  mathscinet  zmath  adsnasa  isi
10. M. Bellassoued, M. Choulli, “Logarithmic stability in the dynamical inverse problem for the Schrödinger equation by arbitrary boundary observation”, J. Math. Pures Appl., 91 (2009), 233–255  crossref  mathscinet  zmath  isi
11. M. Belishev, “Dynamical systems with boundary control: models and characterization of inverse data”, Inverse Problems, 17:4 (2001), 659–682  crossref  mathscinet  zmath  adsnasa  isi
12. M. Belishev, “On a relation between data of dynamic and spectral inverse problems”, Zap. Nauchn. Semin. POMI, 297, 2003, 30–48  mathnet  mathscinet  zmath
13. M. Belishev, “Recent progress in the boundary control method”, Inverse Problems, 23:5 (2007), R1–R67  crossref  mathscinet  zmath  isi
14. A. Mercado, A. A. Osses, L. Rosier, “Carleman inequalities and inverse problems for the Schrödinger equation”, C. R. Acad. Sci. Paris, Ser. I, 346 (2008), 53–58  crossref  mathscinet  zmath  isi
15. K. Ramdani, M. Tucsnak, G. Weiss, “Recovering the initial state of an infinite-dimensional system using observers”, Automatica, 46 (2010), 1616–1625  crossref  mathscinet  zmath  isi  elib
16. M. Tucsnak, G. Weiss, Observation and control for operator semigroups, Birkhaüser Advanced Texts, Basler Lehrbucher [Birkhaüser Advanced Texts, Basel Textbooks], Birkhaüser Verlag, Basel, 2009, xii+483 pp.  mathscinet  zmath
17. M. Yamamoto, “Stability, reconstruction formula and regularization for an inverse source hyperbolic problem by a control method”, Inverse Problems, 11:2 (1995), 481–496  crossref  mathscinet  zmath  adsnasa  isi


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