Author | Ramm, Alexander G. author |
---|---|
Title | Scattering by Obstacles [electronic resource] / by Alexander G. Ramm |
Imprint | Dordrecht : Springer Netherlands, 1986 |
Connect to | http://dx.doi.org/10.1007/978-94-009-4544-9 |
Descript | 444p. online resource |
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 Helmholtzโs Equation for Large frequencies -- 7. Representations of solutions to Helmholtzโs 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