(Ebook) Ill Posed and Inverse Problems Dedicated to Academician Mikhail Mikhailovich Lavrentiev on the Occasion of his 70th Birthday 1st Edition by Vladimir G Romanov, Sergey I Kabanikhin, Yurii E Anikonov, A L Bukhgeim ISBN 3110942011 9783110942019

(Ebook) Ill Posed and Inverse Problems Dedicated to Academician Mikhail Mikhailovich Lavrentiev on the Occasion of his 70th Birthday 1st Edition by Vladimir G Romanov, Sergey I Kabanikhin, Yurii E Anikonov, A L Bukhgeim ISBN 3110942011 9783110942019

(Ebook) Ill Posed and Inverse Problems Dedicated to Academician Mikhail Mikhailovich Lavrentiev on the Occasion of his 70th Birthday 1st Edition by Vladimir G Romanov, Sergey I Kabanikhin, Yurii E Anikonov, A L Bukhgeim - Ebook PDF Instant Download/Delivery: 3110942011, 9783110942019
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ISBN 10: 3110942011 
ISBN 13: 9783110942019
Author: Vladimir G Romanov, Sergey I Kabanikhin, Yurii E Anikonov, A L Bukhgeim

In 1968 Lavrentiev was elected as a corresponding member of the Academy of Sciences, and in 1981 as an academician. In 1987 Μ. M. Lavrentiev and his colleagues V. G. Romanov, Yu. E. Anikonov, V. R. Kireitov and S. P. Shishatsky were awarded the state prize for the results in the theory of inverse and ill-posed problems. For his activity as a scientist and professor Μ. M. Lavrentiev was awarded several other state prizes as well. Since 1986 Lavrentiev has been the director of the Sobolev Institute of Mathematics of Siberian Branch of the Russian Academy of Sciences. The last 15 years were extremely difficult for the institute because of perestroika and financial problems. Due to his organization experience and activity the institute holds high position in the science and is successfully developing. All leading scientific schools keep working. Many new doctoral and candidate dissertations have been defended during the last 15 years. Μ. M. Lavrentiev is the author of many fundamental scientific results in many directions of mathematics and its applications, namely, in differential equations, inverse and ill-posed problems, tomography, numerical and applied mathematics. A. N. Tikhonov, V. K. Ivanov and Μ. M. Lavrentiev created a new scientific direction of modern mathematics — the theory of ill-posed problems of mathematical physics and analysis, which is of considerable theoretical and practical value. By ill-posed problems are meant the problems which do not satisfy one of the classical well-posedness conditions such as uniqueness, existence and stability of the solution. Ill-posed problems are usually unstable with respect to small variations of data. A wellknown example is the Cauchy problem for Laplace equation. It turns out that some a priori information about the ill-posed problem solution makes the solution stable and allows one to construct approximations with an arbitrary accuracy. This fact was remarked by Academician A. N. Tikhonov in 1943 for an inverse problem of potential. Thus ill-posed problems become theoretically and practically valuable provided some a priori information concerning their solutions is given. Taking into account this fact Μ. M. Lavrentiev introduced the concept of a conditionally well-posed problem (Tikhonov well-posedness). The solution of conditionally well posed problems (or a well-posed problem in the sense of Tikhonov) is stable with respect to those variations of data which keep the solution in a priori given

(Ebook) Ill Posed and Inverse Problems Dedicated to Academician Mikhail Mikhailovich Lavrentiev on the Occasion of his 70th Birthday 1st Table of contents:

1. Representations of Functions of Many Complex Variables and Inverse Problems for Kinetic Equations

2. Uniqueness in Determining Piecewise Analytic Coefficients in Hyperbolic Equations

3. Direct and Inverse Problems for Evolution Integro-Differential Equations of the First-Order in Time

4. How to See Waves Under the Earth Surface (The BC-Method for Geophysicists)

5. Global Theorem of Uniqueness of Solution to Inverse Coefficient Problem for a Quasilinear Hyperbolic Equation

6. Identification of Parameters in Polymer Crystallization, Semiconductor Models and Elasticity via Iterative Regularization Methods

7. The Tomato Salad Problem in Spherical Stereology

8. Two Methods in Inverse Problem and Extraction Formulae

9. Identification of the Unknown Potential in the Nonstationary Schrödinger Equation

10. Iterative Methods of Solving Inverse Problems for Hyperbolic Equations

11. Carleman Estimates and Inverse Problems: Uniqueness and Convexification of Multiextremal Objective Functions

12. Convergence Analysis of a Landweber—Kaczmarz Method for Solving Nonlinear Ill-Posed Problems

13. A Sampling Method for an Inverse Boundary Value Problem for Harmonic Vector Fields

14. Approaching a Partial Differential Equation of Mixed Elliptic-Hyperbolic Type

15. Complex Geometrical Optics Solutions and Pseudoanalytic Matrices

16. Numerical Solution of Inverse Evolution Problems via the Nonlinear Levitan Equation

17. An Inverse Problem for a Parabolic Equation with Final Overdetermination

18. Uniqueness Theorems for an Inverse Problem Related to Local Heterogeneities and Data on a Piece of a Plane

19. On Ill-Posed Problems and Professor Lavrentiev

20. Regularization and Iterative Approximation for Linear Ill-Posed Problems in the Space of Functions of Bounded Variation

21. A Posteriori Error Estimation for Ill-Posed Problems on Some Sourcewise Represented or Compact Sets

22. Multidimensional Inverse Problems for Hyperbolic Equations with Point Sources

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Tags: Vladimir G Romanov, Sergey I Kabanikhin, Yurii E Anikonov, A L Bukhgeim, Problems, Academician