Forward and inverse problems for hyperbolic, elliptic, and mixed type equations / A.G. Megrabov.

Format:

Book

Author/Creator:

Megrabov, A. G.

Series:

Inverse and ill-posed problems series

Inverse and Ill-Posed Problems Series ; 40

Language:

English

Subjects (All):

Differential equations, Partial--Numerical solutions.

Differential equations, Partial.

Inverse problems (Differential equations)--Numerical solutions.

Inverse problems (Differential equations).

Physical Description:

1 online resource (242 pages) : illustrations.

Edition:

Reprint 2012

Place of Publication:

Utrecht ; Boston : VSP, 2003.

Language Note:

English

Summary:

Inverse problems are an important and rapidly developing direction in mathematics, mathematical physics, differential equations, and various applied technologies (geophysics, optic, tomography, remote sensing, radar-location, etc.). In this monograph direct and inverse problems for partial differential equations are considered. The type of equations focused are hyperbolic, elliptic, and mixed (elliptic-hyperbolic). The direct problems arise as generalizations of problems of scattering plane elastic or acoustic waves from inhomogeneous layer (or from half-space). The inverse problems are those of determination of medium parameters by giving the forms of incident and reflected waves or the vibrations of certain points of the medium. The method of research of all inverse problems is spectral-analytical, consisting in reducing the considered inverse problems to the known inverse problems for the Sturm-Liouville equation or the string equation. Besides the book considers discrete inverse problems. In these problems an arbitrary set of point sources (emissive sources, oscillators, point masses) is determined.

Contents:

Frontmatter

Preface

Contents

Introduction

Chapter 1. Inverse problems for semibounded string with the directional derivative condition given in the end

Chapter 2. Inverse problems for the elliptic equation in the half-plane

Chapter 3. Inverse problems of scattering plane waves from inhomogeneous transition layers (half-space)

Chapter 4. Inverse problems for finite string with the condition of directional derivative in one end

Chapter 5. Inverse problems for the elliptic equation in the strip

Chapter 6. Inverse problems of scattering the plane waves from inhomogeneous layers with a free or fixed boundary

Chapter 7. Direct and inverse problems for the equations of mixed type

Chapter 8. Inverse problems connected with determination of arbitrary set of point sources

Bibliography

Notes:

Bibliographic Level Mode of Issuance: Monograph

Includes bibliographical references (pages [221]-230).

Description based on print version record.

ISBN:

9783110944983

3110944987

OCLC:

979607416