Inverse Problems of Mathematical Physics
1st Edition
Will be published approx. on 1. December 1986
Book
Hardback
VIII, 239 pages
978-90-6764-056-5 (ISBN)
Description
01/07 This title is now available from Walter de Gruyter. Please see www.degruyter.com for more information.
This book surveys basic features of the comparatively newly emerged theory of inverse problems for equations of mathematical physics, i.e. of the problems aimed at defining the coeficients of a differential equation through some functionals of its solution. This kind of problem arises in various fields of science when trying to describe internal characteristics of a substance where physico-chemical processes take place by the results of observing these processes within the available range of measurements.
The book offers in-depth coverage of inverse problems for second-order equations and for hyperbolic systems of first-order equations, including the kinematic problem of seismology, the Lamb dynamic problem for equations of the theory of elasticity, and the problem of electrodynamics.
This book surveys basic features of the comparatively newly emerged theory of inverse problems for equations of mathematical physics, i.e. of the problems aimed at defining the coeficients of a differential equation through some functionals of its solution. This kind of problem arises in various fields of science when trying to describe internal characteristics of a substance where physico-chemical processes take place by the results of observing these processes within the available range of measurements.
The book offers in-depth coverage of inverse problems for second-order equations and for hyperbolic systems of first-order equations, including the kinematic problem of seismology, the Lamb dynamic problem for equations of the theory of elasticity, and the problem of electrodynamics.
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Inverse Problems of Mathematical Physics
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V. G. Romanov
Inverse Problems of Mathematical Physics
Book
12/1986
1st Edition
De Gruyter
€250.00
Shipment within 7-9 days
Content
Foreword by V.G. Yakhno
INTRODUCTION
Inverse problem concept: examples of formulating inverse problems
On correctness of direct and inverse problems of mathematical physics
INVERSE PROBLEMS FOR THE OPERATOR #TEX2HTML_WRAP_INLINE3211#
Problems with nonfocused initial data
Some aspects associated with the inverse problem for the equation
Problems with a focused source of disturbance
Reducing the problem with a focused source of disturbance to a linear, integral equation: necessary and sufficient conditions for the inverse problem solvability
Inverse problems for differential equations in a limited domain
Relationship with the Sturm--Liouville problem
One-dimensional inverse problems for second-order linear hyperbolic equations
Problem of determining the operator in a second-order hyperbolic equation
INVERSE KINEMATIC PROBLEMS IN SEISMOLOGY
Iconical equations, rays, and fronts
Boundary rays; waveguides: a sufficient condition for the absence of waveguides and boundary rays-ray regularity
One-dimensional inverse kinematic problems
Linearized three-dimensional inverse problems
Nonlinear three-dimensional inverse problems
Inverse problems using inner sources
Inverse kinematic problems for an anisotropic medium
SECOND-ORDER EQUATIONS OF A HYPERBOLIC TYPE AND RELATED INVERSE PROBLEMS
Fundamental solution and its differential properties
Ray formulation of inverse problems for the coefficients at minor derivatives
Inverse dynamic problem: linearization method
General scheme of studying inverse problems for hyperbolic type equations
INVERSE PROBLEMS FOR FIRST-ORDER LINEAR HYPERBOLIC SYSTEMS
Systems of equations with a single spatial variable
Inverse problems using focused sources of wave generation
Problem of determining the right-hand part of a hyperbolic system
Lamb one-dimensional inverse problem
Lamb three-dimensional inverse problem within a linear approach
Inverse problem for a system of Maxwell equations
INVERSE PROBLEMS FOR PARABOLIC AND ELLIPTICAL TYPE SECOND-ORDER EQUATIONS
Problem of determining the density of heat sources
Problem of determining diffusion coefficients
Relations among inverse problems for parabolic, elliptical, and hyperbolic type equations
On specific formulations of inverse problems where the coefficient to be determined is independent of one of the variables
References
Index
INTRODUCTION
Inverse problem concept: examples of formulating inverse problems
On correctness of direct and inverse problems of mathematical physics
INVERSE PROBLEMS FOR THE OPERATOR #TEX2HTML_WRAP_INLINE3211#
Problems with nonfocused initial data
Some aspects associated with the inverse problem for the equation
Problems with a focused source of disturbance
Reducing the problem with a focused source of disturbance to a linear, integral equation: necessary and sufficient conditions for the inverse problem solvability
Inverse problems for differential equations in a limited domain
Relationship with the Sturm--Liouville problem
One-dimensional inverse problems for second-order linear hyperbolic equations
Problem of determining the operator in a second-order hyperbolic equation
INVERSE KINEMATIC PROBLEMS IN SEISMOLOGY
Iconical equations, rays, and fronts
Boundary rays; waveguides: a sufficient condition for the absence of waveguides and boundary rays-ray regularity
One-dimensional inverse kinematic problems
Linearized three-dimensional inverse problems
Nonlinear three-dimensional inverse problems
Inverse problems using inner sources
Inverse kinematic problems for an anisotropic medium
SECOND-ORDER EQUATIONS OF A HYPERBOLIC TYPE AND RELATED INVERSE PROBLEMS
Fundamental solution and its differential properties
Ray formulation of inverse problems for the coefficients at minor derivatives
Inverse dynamic problem: linearization method
General scheme of studying inverse problems for hyperbolic type equations
INVERSE PROBLEMS FOR FIRST-ORDER LINEAR HYPERBOLIC SYSTEMS
Systems of equations with a single spatial variable
Inverse problems using focused sources of wave generation
Problem of determining the right-hand part of a hyperbolic system
Lamb one-dimensional inverse problem
Lamb three-dimensional inverse problem within a linear approach
Inverse problem for a system of Maxwell equations
INVERSE PROBLEMS FOR PARABOLIC AND ELLIPTICAL TYPE SECOND-ORDER EQUATIONS
Problem of determining the density of heat sources
Problem of determining diffusion coefficients
Relations among inverse problems for parabolic, elliptical, and hyperbolic type equations
On specific formulations of inverse problems where the coefficient to be determined is independent of one of the variables
References
Index