Inverse Problems of Mathematical Physics
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Inverse Problems of Mathematical Physics

Inverse Problems of Mathematical Physics

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About the Book

Thismonograph deals with the theory of inverse problems of mathematical physics andapplications of such problems. Besides it considers applications and numerical methods of solving the problems under study. Descriptions of particular numerical experiments are also included.

Table of Contents:
Introduction The concept of mathematical simulation Direct and inverse problems On correctness of direct and inverse problems of mathematical physics Chapter 1. Some physical motivations of inverse problems Inverse problems of geophysics Inverse tomography problems Chapter 2. Approximate methods of solution of ill-posed problems On some aspects of statement and solution of ill-posed problems Solutions on compact sets. The concept of a quasi-solution The method of quasi-inversion Regularization methods Chapter 3. Integral geometry problems Statement of integral geometry problems The Radon problem The problem of general form on the plane Problems of general form in the space Problems of Volterra type with manifolds invariant under the motion group Integral geometry problems with perturbation on the plane Mathematical problems of tomography and hyperbolic mappings Chapter 4. One dimensional inverse problems Some inverse problems for Lamé system Inverse problems for quasi-stationary Maxwell’s equations Connections among inverse problems of hyperbolic, elliptic and parabolic type Problems with a focused source of disturbances Reducing the problem with a focused source of disturbances to a linear integral equation: necessary and sufficient conditions for solvability of the inverse problems Determination of the piece-wise constant coefficient for wave equation Chapter 5. Inverse problems for the coupled Maxwell and Lamé systems One-dimensional inverse problem of electromagnetoelasticity in the case of the seismomagnetic effect Inverse problems of electromagnetoelasticity in the case of piezoelectric interaction Inverse problems of electromagnetoelasticity for weakly conducting media An inverse problem of electromagnetoelasticity in the case of nonlinear interaction Chapter 6. Numerical solution of inverse problems: some examples Short review of numerical approaches to solving inverse problems Numerical solution of a 3D inverse kinematic problem of seismics Determination of the structure of the Earth’s upper mantle Numerical solution of inverse problems of electromagnetoelasticity Simulation of the long-term coastal profile evolution Bibliography


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Product Details
  • ISBN-13: 9789067643962
  • Publisher: Brill
  • Publisher Imprint: VSP International Science Publishers
  • Language: English
  • Weight: 635 gr
  • ISBN-10: 9067643963
  • Publisher Date: 27 Sep 2003
  • Binding: Hardback
  • No of Pages: 281


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