Scattering by obstacles

A.G. Ramm


  • I. Scattering by an Obstacle.- 1. Statement of the Problem. Basic Integral Equations.- 2. Existence and Uniqueness of the Solution to the Scattering Problem.- 3. Eigenfunction Expansion Theorem.- 4. Properties of the Scattering Amplitude.- 5. The S-Matrix and Wave Operators.- 6. Inequalities for Solutions to Helmholtz's Equation for Large frequencies.- 7. Representations of solutions to Helmholtz's Equation.- II. The Inverse Scattering (Diffraction) Problem.- 1. Statement of the Problem and Uniqueness Theorems.- 2. Reconstruction of Obstacles from the Scattering Data at High Frequencies.- 3. Stability of the Surface with Respect to Small Perturbations of the Data.- III. Time Dependent Problem.- 1. Statement of the Problems.- 2. The Limiting Amplitude Principle (Abstract Results).- 3. The Limiting Amplitude Principle for the Laplacian in Exterior Domains.- 4. Decay of Energy.- 5. Singularity and Eigenmode Expansion Methods.- IV. T-Matrix Scheme and Other Numerical Schemes.- 1. Statement of the Problem.- 2. Justification of the T-Matrix Scheme.- 3. Numerical Results.- 4. Other Schemes.- V. Scattering by Small Bodies.- 1. Scattering by a Single Small Body.- 2. Scattering by Many Small Bodies.- 3. Electromagnetic Wave Scattering by Small Bodies.- 4. Behavior of the Solutions to Exterior Boundary Value Problems at Low Frequencies.- VI. Some Inverse Scattering Problems of Geophysics.- 1. Inverse Scattering for Geophysical Problems.- 2. Two Parameter Inversion.- 3. An Inversion Formula in Scattering Theory.- 4. A Model Inverse Problem of Induction Logging.- VII. Scattering by Obstacles with Infinite Boundaries.- 1. Statement of the Problem.- 2. Spectral Properties of the Laplacians.- 3. Spectral Properties of the Dirichlet Laplacian in Semi-Infinite Tubes.- 4. Absence of Positive Eigenvalues for the Dirichlet Laplacian Under Local Assumptions at Infinity.- 5. The Limiting Absorption Principle and Compact Perturbations of the Boundary.- 6. Eigenfunction Expansions in Canonical Domains.- Appendix 1. Summary of some Results in Potential Theory and Embedding Theorems.- Appendix 2. Summary of some Results in Operator Theory.- Appendix 4. Stable Numerical Differentiation.- Appendix 5. Limit of the Spectra of the Interior Neumann Problems when a Solid Domain Shrinks to a Plane One.- Appendix 6. Construction of a Surface from its Principal Curvatures.- Appendix 7. Resonances.- Research Problems.- Bibliographical Notes.- List of Symbols.

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書名 Scattering by obstacles
著作者等 Ramm, Alexander G.
Ramm A.G.
シリーズ名 Mathematics and its applications
出版元 D.Reidel
Sold and Kluwer Academic
刊行年月 c1986
ページ数 xiv, 423 p.
大きさ 23 cm
ISBN 9027721033
NCID BA00134281
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言語 英語
出版国 オランダ

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