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Multidimensional Inverse and Ill-Posed Problems for Differential Equations / Yu. E. Anikonov.

By: Material type: TextTextLanguage: English Series: Inverse and Ill-Posed Problems Series ; 4Publisher: Berlin ; Boston : De Gruyter, [2014]Copyright date: ©1995Edition: Reprint 2014Description: 1 online resource (133 p.)Content type:
  • text
Media type:
  • computer
Carrier type:
  • online resource
ISBN:
  • 9783110271478
Subject(s): Additional physical formats: No titleOnline resources: Available additional physical forms:
  • Issued also in print.
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
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.
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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

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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.

Issued also in print.

Mode of access: Internet via World Wide Web.

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

In English.

Description based on online resource; title from PDF title page (publisher's Web site, viewed 01. Dez 2022)

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