Multidimensional inverse and ill-posed problems for differential equations / Yu.E. Anikonov.

Format:

Book

Author/Creator:

Anikonov, I︠U︡. E. (I︠U︡riĭ Evgenʹevich), author.

Series:

Inverse and ill-posed problems series.

Inverse and ill-posed problems series

Language:

English

Subjects (All):

Inverse problems (Differential equations).

Differential equations.

Physical Description:

1 online resource (140 pages).

Edition:

Reprint 2014

Place of Publication:

Utrecht, The Netherlands : VSP, 1995.

Language Note:

In English.

Summary:

Inverse problems are usually nonlinear and are separated into one-dimensional and multidimensional problems, depending on whether the sought function (or functions) is a function of one variable or of many. Multidimensionality of inverse problems has particular value at present, because practice shows that many investigating processes are described by an equation, of which the co-efficient essentially depends on many variables. This monograph is devoted to statements of multidimensional inverse problems, in particular to methods of their investigation. Questions of the uniqueness of solution, solvability and stability are studied. Methods to construct a solution are given and, in certain cases, inversion formulas are given as well. Concrete applications of the theory developed here are also given. Where possible, the author has stopped to consider the method of investigation of the problems, thereby sometimes losing generality and quantity of the problems, which can be examined by such a method. The book should be of interet to researchers in the field of applied mathematics, geophysics and mathematical biology.

Contents:

Frontmatter

CONTENTS

INTRODUCTION

CHAPTER 1. Operator Equations and Inverse Problems

CHAPTER 2. Inverse Problems for Kinetic Equations

CHAPTER 3. Geometry of Convex Surfaces in the Large and Inverse Problems of Scattering Theory

CHAPTER 4. Integral Geometry

References

Notes:

Includes bibliographical references.

This eBook is made available Open Access under a CC BY-NC-ND 4.0 license: https://creativecommons.org/licenses/by-nc-nd/4.0 https://www.degruyter.com/dg/page/open-access-policy

Description based on online resource; title from PDF title page (ebrary, viewed January 26, 2015).

ISBN:

9783110271478

3110271478

OCLC:

1013954638

Access Restriction:

Open Access Unrestricted online access