Speciality:
01.01.03 (Mathematical physics)
Birth date:
29.07.1949
E-mail: Keywords: inverse problems of mathematical physics; dynamical and spectral inverse problems; multidimensional inverse problems of acoustics, electrodynamics, elasticity; boundary control theory and its relations with inverse problems; general linear system theory; questions on operator theory related with inverse problems; theory of operator models in connection with inverse problems.
Subject:
A new approach to the inverse problems based upon their relations with the boundary control theory (the so-called BC-method) was created. The approach is of complex character: besides the control theory, the asymptotic methods (Geometrical Optics, propagation of singularities), the functional analysis (triangular factorization of operators, operator integral), and the general linear system theory (models, canonical realizations) are in use. The BC-method permits to reconstruct the Riemannian manifold of arbitrary dimension and topology trough its spectral or dynamical (wave, heat, electromagnetic) boundary data. In the case of dynamical data the reconstruction by the BC-method is time-optimal: the longer is time of observations at the boundary, the bigger is the depth of reconstruction, that is essential in applications. The algorithms based upon the BC-method demonstrate their efficiency in numerical testing.
Main publications:
M. I. Belishev. Boundary control in reconstruction of manifolds and metrics (the BC-method) // Inverse Problems, 1997, 13(5), R1–R45.
М. И. Белишев, В. М. Исаков, Л. Н. Пестов, В. А. Шарафутдинов. К реконструкции метрики по внешним электромагнитным измерениям // ДАН РАН, 2000, 372(3), 298–300.
M. I. Belishev and A. K. Glasman. Dynamical inverse problem for the Maxwell system: recovering the velocity in regular zone (the BC-method) // St. Petersburg Math. J., 2001, 12(2), 279–316.
M. I. Belishev. Dynamical systems with boundary control: models and characterization of inverse data // Inverse Problems, 2001, 17, 659–682.
M. I. Belishev. On relations between spectral and dynamical inverse data // J. Inv. Ill-Posed Problems, 2001, 9(6), 1–18.
