Inverse Problems for Partial Differential Equations

✍ Scribed by Yurii Ya. Belov

• Publisher: De Gruyter
• Year: 2012
• Tongue: English
• Leaves: 220
• Series: Inverse and Ill-Posed Problems Series; 32
• Edition: Reprint 2012
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

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