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Integral Geometry and Inverse Problems for Hyperbolic Equations

BuchKartoniert, Paperback
154 Seiten
Englisch
Springererschienen am19.01.2012Softcover reprint of the original 1st ed. 1974
These are often called "inverse problems of mathematical physics" and may be contrasted with problems in which an equation is given and one looks for its solution under initial and boundary conditions.mehr

Produkt

KlappentextThese are often called "inverse problems of mathematical physics" and may be contrasted with problems in which an equation is given and one looks for its solution under initial and boundary conditions.
Details
ISBN/GTIN978-3-642-80783-1
ProduktartBuch
EinbandartKartoniert, Paperback
Verlag
Erscheinungsjahr2012
Erscheinungsdatum19.01.2012
AuflageSoftcover reprint of the original 1st ed. 1974
ReiheSpringer Tracts in Natural Philosophy
Seiten154 Seiten
SpracheEnglisch
Gewicht270 g
IllustrationenVI, 154 p.
Artikel-Nr.18233168

Inhalt/Kritik

Inhaltsverzeichnis
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 Earth´s Structure from a Geophysical Standpoint and the Problem of Determining the Velocity Structure of the Earth´s Mantle.- 2. Numerical Solution of the Linearized Inverse Kinematic Problem.- 3. Some Numerical Results.mehr