Coefficient inverse problems for parabolic type equations and their application / P.G. Danilaev.

Format:

Book

Author/Creator:

Danilaev, P. G., author.

Series:

Inverse and ill-posed problems series.

Inverse and ill-posed problems series, 1381-4524

Language:

English

Subjects (All):

Differential equations, Parabolic--Numerical solutions.

Differential equations, Parabolic.

Inverse problems (Differential equations)--Numerical solutions.

Inverse problems (Differential equations).

Physical Description:

1 online resource (125 pages) : illustrations.

Edition:

Reprint 2014

Place of Publication:

Utrecht ; Boston : VSP, 2001.

Language Note:

English

Summary:

As a rule, many practical problems are studied in a situation when the input data are incomplete. For example, this is the case for a parabolic partial differential equation describing the non-stationary physical process of heat and mass transfer if it contains the unknown thermal conductivity coefficient. Such situations arising in physical problems motivated the appearance of the present work. In this monograph the author considers numerical solutions of the quasi-inversion problems, to which the solution of the original coefficient inverse problems are reduced. Underground fluid dynamics is taken as a field of practical use of coefficient inverse problems. The significance of these problems for this application domain consists in the possibility to determine the physical fields of parameters that characterize the filtration properties of porous media (oil strata). This provides the possibility of predicting the conditions of oil-field development and the effects of the exploitation. The research carried out by the author showed that the quasi-inversion method can be applied also for solution of "interior coefficient inverse problems" by reducing them to the problem of continuation of a solution to a parabolic equation. This reduction is based on the results of the proofs of the uniqueness theorems for solutions of the corresponding coefficient inverse problems.

Contents:

Front matter

Contents

Preface

Chapter 1. On the ill-posedness of coefficient inverse problems and the general approach to the study of them

Chapter 2. Determining the coefficient of the lowest term of equation

Chapter 3. Determining of the coefficient for the leading terms of equation

Chapter 4. Modification of the method of determining the coefficient of the leading terms in an equation

Chapter 5. Generalizations of the developed algorithm for solving coefficient inversion problems

Chapter 6. On applications of coefficient inverse problems in underground fluid dynamics

Summary

Bibliography

Notes:

Bibliographic Level Mode of Issuance: Monograph

Includes bibliographical references.

Description based on print version record.

ISBN:

9783110940916

3110940914

OCLC:

1013963414