Author | Romanov, V. G. author |
---|---|
Title | Integral Geometry and Inverse Problems for Hyperbolic Equations [electronic resource] / by V. G. Romanov |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg, 1974 |
Connect to | http://dx.doi.org/10.1007/978-3-642-80781-7 |
Descript | VI, 154 p. online resource |
I. Some Problems in Integral Geometry -- 1. Problem of Finding a Function from its Integrals over Ellipsoids of Revolution -- 2. Generalization to the Case of Analytic Curves -- 3. Existence Theorem for the Case of Ellipses -- 4. Determination of a Function from its Integrals over a Family of Curves Invariant to Displacement -- 5. The Integral-Geometric Problem for m Functions -- 6. Determination of a Function in a Circle from its Integrals over a Family of Curves Invariant to Rotation about Center of the Circle -- 7. Integral-Geometric Problem for Surfaces Invariant to Displacement -- 8. Integral-Geometric Problems for a Family of Curves Generated by a Riemannian Metric -- II. Inverse Problems for Hyperbolic Linear Differential Equations -- 1. General Information Concerning the Solution of the Cauchy Problem for Linear Hyperbolic Equations -- 2. One-Dimensional Inverse Problem for the Telegraph Equation in Three-Dimensional Space -- 3. Linearized Inverse Problem for the Telegraph Equation -- 4. The Problem of Finding the Coefficients of the Lower Order Derivatives in a Second-Order Equation -- 5. Linearized Inverse Kinematic Problem for the Wave Equation in Variable Isotropic Media -- 6. One-Dimensional Inverse Kinematic Problem for the Wave Equation in Anisotropic Media -- 7. Multidimensional Linearized Inverse Kinematic Problem for the Wave Equation in Anisotropic Media -- III. Application of the Linearized Inverse Kinematic Problem to Geophysics -- 1. The Earthโs Structure from a Geophysical Standpoint and the Problem of Determining the Velocity Structure of the Earthโs Mantle -- 2. Numerical Solution of the Linearized Inverse Kinematic Problem -- 3. Some Numerical Results