Inverse problems for partial differential equations / Yu. Ya. Belov.

Format:

Book

Author/Creator:

Belov, Yu. Ya, author.

Series:

Inverse and ill-posed problems series.

Inverse and Ill-Posed Problems Series

Language:

English

Subjects (All):

Differential equations, Partial.

Inverse problems (Differential equations).

Mathematical physics.

Physical Description:

1 online resource (219 p.)

Edition:

Reprint 2012

Place of Publication:

Utrecht, [The Netherlands] : VSP, 2002.

Language Note:

English

Summary:

This monograph is devoted to identification problems of coefficients in equations of mathematical physics. It invesitgates the existence and uniqueness of the solutions for identification coefficient problems in parabolic and hyperbolic equations and equation systems of composite type. The problems are studied with the Cauchy data and equations in which the Fourier transform with respect to the chosen variable is supposed to occur. Differential properties of the solutions for the original direct problems and their behavior under great values of time are studied on the basis of solution properties for direct problems. The identification problems with one or two unknown coefficients are also investigated. For initial boundary value conditions linear and nonlinear parabolic equations are studied.

Contents:

Frontmatter

Preface

Contents

Chapter 1. Auxiliary information from functional analysis and theory of differential equations

Chapter 2. The weak approximation method

Chapter 3. Identification problems for parabolic equations with Cauchy data

Chapter 4. The identification of the source function for a system of composite type and parabolic equation. The behavior of the problem's solution under t -> + ∞

Chapter 5. The problem of determining the coefficient in a parabolic equation and some properties of its solution

Chapter 6. Two unknown coefficients of a parabolic type equation

Chapter 7. Some inverse boundary value problems

Bibliography

Notes:

Description based upon print version of record.

Includes bibliographical references.

Description based on print version record.

ISBN:

9783110944631

3110944634

OCLC:

979589223