Reachable sets of a Lamé type dynamical system
- 59 Downloads
By a version of the boundary control method (Belishev, 1986), a Riemannian manifold is recovered via its dynamical boundary inverse data, which correspond to the scalar wave equation, with the help of the virtual sources. We extend this version to the dynamical vector Lamé-type system. Such an extension is based on studying the structure of the reachable sets. The prospective goal of our study is to solve the inverse problem of recovering parameters of the Lamé system from the dynamical boundary data. Bibliography: 13 titles. Illustrations: 3 figures.
KeywordsInverse Problem Riemannian Manifold Type System Boundary Control Virtual Source
Unable to display preview. Download preview PDF.
- 3.M. I. Belishev, “On the reconstruction of a Riemannian manifold from boundary data: the theory and plan of a numerical experiment” [in Russian], Zap. Nauchn. Semin. POMI 380, 8–30 (2010); English transl.: J. Math. Sci., New York 175, No. 6, 623–636 (2011).Google Scholar
- 6.O. A. Ladyzhenskaya, The Mathematical Theory of Viscous Incompressible Flow [in Russian], Nauka, M. (1970); English transl.: Gordon and Breach, New York (1964).Google Scholar
- 8.V. G. Fomenko, “The reaction operator of the Lamé system” [in Russian], Skladn. Sist. Protses. No. 1, 13–18 (2010).Google Scholar
- 10.M. Eller, V. Isakov, G. Nakamura, and D. Tataru, “Uniqueness and stability in the Cauchy problem for Maxwell’s and elasticity systems”, In: Nonlinear Partial Differential Equations and Their Applications, pp. 329–349, Elsevier, Amsterdam (2002).Google Scholar
- 12.M. I. Belishev and A. S. Blagoveschenskii, Dynamical Inverse Problems un the Wave Theory [in Russian], St.-Petersb. State Univ. Press, St.-Petersb. (1999).Google Scholar