eBook ISBN:  9781470433413 
Product Code:  TRANS2/130.E 
List Price:  $89.00 
MAA Member Price:  $80.10 
AMS Member Price:  $71.20 
eBook ISBN:  9781470433413 
Product Code:  TRANS2/130.E 
List Price:  $89.00 
MAA Member Price:  $80.10 
AMS Member Price:  $71.20 

Book DetailsAmerican Mathematical Society Translations  Series 2Volume: 130; 1986; 70 ppMSC: Primary 35;
This monograph deals with the inverse problems of determining a variable coefficient and right side for hyperbolic and parabolic equations on the basis of known solutions at fixed points of space for all times. The problems are onedimensional in nature since the desired coefficient of the equation is a function of only one coordinate, while the desired right side is a function only of time. The authors use methods based on the spectral theory of ordinary differential operators of second order and also methods which make it possible to reduce the investigation of the inverse problems to the investigation of nonlinear operator equations. The problems studied have applied importance, since they are models for interpreting data of geophysical prospecting by seismic and electric means.
In the first chapter the authors prove the onetoone correspondence between solutions of direct Cauchy problems for equations of different types, and they present the solution of an inverse problem of heat conduction. In the second chapter they consider a secondorder hyperbolic equation describing a wave process in threedimensional halfspace. The third chapter investigates formulations of onedimensional inverse problems for the wave equation in multidimensional space.

Table of Contents

Chapters

Introduction

Solutions of direct and inverse problems and some of their relations

Source problems

A onedimensional inverse problem for the wave equation

Appendix


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This monograph deals with the inverse problems of determining a variable coefficient and right side for hyperbolic and parabolic equations on the basis of known solutions at fixed points of space for all times. The problems are onedimensional in nature since the desired coefficient of the equation is a function of only one coordinate, while the desired right side is a function only of time. The authors use methods based on the spectral theory of ordinary differential operators of second order and also methods which make it possible to reduce the investigation of the inverse problems to the investigation of nonlinear operator equations. The problems studied have applied importance, since they are models for interpreting data of geophysical prospecting by seismic and electric means.
In the first chapter the authors prove the onetoone correspondence between solutions of direct Cauchy problems for equations of different types, and they present the solution of an inverse problem of heat conduction. In the second chapter they consider a secondorder hyperbolic equation describing a wave process in threedimensional halfspace. The third chapter investigates formulations of onedimensional inverse problems for the wave equation in multidimensional space.

Chapters

Introduction

Solutions of direct and inverse problems and some of their relations

Source problems

A onedimensional inverse problem for the wave equation

Appendix