Scattering by Obstacles and Potentials

The book is important as it contains results many of which are not available in the literature, except in the author's papers. Among other things, it gives uniqueness theorems for inverse scattering problems when the data are non-over-determined, numerical method for solving inverse scattering problems, a method (MRC) for solving direct scattering problem.

Contents:

• Scattering by Obstacles:

  • Scattering by an Obstacle
  • The Inverse Scattering Problem
  • Time-Dependent Problems
  • The T-matrix Scheme
  • Scattering by Small Bodies
  • Some Inverse Scattering Problems of Geophysics
  • Scattering by Obstacles with Infinite Boundaries

• Scattering by Potentials:

  • Scattering by Potentials

• Modified Rayleigh Conjecture (MRC):

  • Modified Rayleigh Conjecture

• Appendices:

  • Summary of Some Results in Potential Theory and Embedding Theorems
  • Summary of Some Results in Operator Theory
  • Eigenfunction Expansions and Asymptotic of the s-Values for Some Nonself-adjoint Operators
  • Stable Numerical Differentiation
  • Limit of the Spectra of the Interior Neumann
  • Recovering of the Surface from the Knowledge of Its Principal Curvatures
  • Calculating Resonances (Natural Frequencies) and Extracting them from Transient Fields

Readership: Researchers and graduate students in mathematics, computational mathematics, physics, acoustics, mechanical engineering.
Key Features:

• It contains material part of which is not available in the literature (except in the author's papers)
• Most of the results belong to the author
• New material is added to the author's earlier monograph "Scattering by obstacles"