Last edited by Goltit
Wednesday, August 5, 2020 | History

3 edition of Multidimensional Inverse & Ill Posed Problems for Differential Equations found in the catalog.

# Multidimensional Inverse & Ill Posed Problems for Differential Equations

## by Yu. E. Anikonov

Written in English

Subjects:
• Applied mathematics,
• Differential equations,
• General,
• Interior Design - General,
• Architecture,
• Science/Mathematics

• The Physical Object
FormatHardcover
Number of Pages134
ID Numbers
Open LibraryOL12849169M
ISBN 109067641855
ISBN 109789067641852

WELCOME, LET THE FUN BEGIN! Get e-Books "Tigra An Iterative Algorithm For Regularizing Nonlinear Ill Posed Problems" on Pdf, ePub, Tuebl, Mobi and Audiobook for are more than 1 Million Books that have been enjoyed by people from all over the world. Always update books hourly, if not looking, search in the book search column. Enjoy % FREE. Download Ill Posed Problems Of Mathematical Physics And Analysis books, Physical formulations leading to ill-posed problems Basic concepts of the theory of ill-posed problems Analytic continuation Boundary value problems for differential equations Volterra equations Integral geometry Multidimensional inverse problems for linear differential.

In order to solve the inverse problems (ill-posed regions of Problems I and ///, entire regions for Problems II and IV) by the method presented in Section 3, it is necessary to add the term y (81T/Btl) to the left-hand sides of equations (la), (13), (15), and t See, for example, Ames [11] or Richtmyer and Morton [12]. CHARLES F. WEBER ( Park, H. M., and Jung, W. S. (Ap ). "On the Solution of Multidimensional Inverse Heat Conduction Problems Using an Efficient Sequential Method.".

The problem of calculating the subsurface characteristic impedance from knowledge of the input pulse and the measured data is the one-dimensional inverse problem of reflection seismology. The problem is set up mathematically as an inverse problem for a first order $2 \times 2$ hyperbolic system. S. I. Kabanikhin, The solvability of inverse problems for differential equations. Soviet Math. Dokl. () 30(1), S.I. Kabanikhin, A projection method for solving multidimensional inverse problems for hyperbolic equations. In: Ill-posed Problems of Mathematical Physics and Analysis, , Nauka, Novosibirsk, (in Russian.

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### Multidimensional Inverse & Ill Posed Problems for Differential Equations by Yu. E. Anikonov Download PDF EPUB FB2

Buy Multidimensional Inverse and Ill-Posed Problems for Differential Equations on FREE SHIPPING on qualified orders Multidimensional Inverse and Ill-Posed Problems for Differential Equations: Anikonov, Yu. E.: : BooksCited by: Get this from a library. Multidimensional inverse and ill-posed problems for differential equations.

[I︠U︡riĭ Evgenʹevich Anikonov]. Frontmatter was published in Multidimensional Inverse and Ill-Posed Problems for Differential Equations on page I. ISBN: OCLC Number: Description: VI, Seiten. Contents: Part 1 Operator equations and inverse problems: definition of quasimonotonicity, the uniqueness theorem; inverse problems for hyperbolic equations; multidimensional inverse kinematic problems of seismics; on the uniqueness of the solution of the Fredholm and Volterra first-kind integral equations.

Citation Information. Multidimensional Inverse and Ill-Posed Problems for Differential Equations. DE GRUYTER. Pages: 86– ISBN (Online): The coupled systems of nonlinear partial differential equations which are used to model the flow of fluids in porous media give rise to several different types of ill-posed and inverse problems.

The mathematical models which describe the fluid flow processes contain function parameters which describe properties of the fluids or properties of. Further, the book can be used as the backbone for a lecture course on inverse and ill-posed problems for partial differential equations.

In turn, the second part of the book. "The first edition of this excellent book appeared in and became a standard reference for everyone interested in analysis and numerics of inverse problems in partial differential equations.

The second edition is considerably expanded and reflects important recent developments in the field. In particular, items 5 and 6 have solved a long standing problem posed by K.

Chadan and P.C. Sabatier in in their book Inverse Problems in Quantum Scattering Theory, Springer-Verlag, New York, In has proposed the first rigorous numerical method for solving ill-posed Cauchy problems for quasilinear PDEs.

The method is an an adaptation. We investigate the mathematical model of the 2D acoustic waves propagation in a heterogeneous domain. The hyperbolic first order system of partial differential equations is considered and solved by the Godunov method of the first order of approximation.

This is a direct problem with appropriate initial and boundary conditions. We solve the coefficient inverse problem (IP) of recovering density. The group focuses on inverse and ill-posed problems of mathematical physics and their applications in various fields of science and industry.

Problems of this kind require research on modern methods of solution of integral and partial differential equations, regularization techniques, and. Basic concepts of ill-posed problem theory; linear Volterra operators and their properties; linear operator Volterra equations; nonlinear operator Volterra equations in the scales of Banach spaces; abstract integro-differential equations and inverse problems; multidimensional inverse problems; multidimensional integro-differential equations of Volterra type; inverse problems of wave.

This allows for studying, for instance, inverse problems modeled by partial differential equations (PDE) [47, 45] and, more generally, infinite-dimensional inverse problems where the measurement. Buy Inverse and Ill-Posed Problems Series, Direct Methods of Solving Multidimensional Inverse Hyperbolic Problems (INVERSE AND ILL-POSED PROBLEMS SERIES, V.

48) on FREE SHIPPING on qualified ordersAuthors: M. Shishlenin, S. Kabanikhin, A. Satybaev. Inverse and Ill-Posed Problems is a collection of papers presented at a seminar of the same title held in Austria in June The papers discuss inverse problems in various disciplines; mathematical solutions of integral equations of the first kind; general considerations for ill-posed problems; and the various regularization methods for integral and operator equations of the first kind.

The backwards diffusion equation is one of the classical ill-posed inverse problems, related to a wide range of applications, and has been extensively studied over the last 50 years. Excerpt: Chapter 2: Well-posed, ill-posed, and inverse problems (p.

15) The purpose of this chapter is to explain the properties that a problem must have to be considered an inverse problem, and to study them in some detail.

We are going to restrict ourselves to linear inverse problems. Unlike ill-posed problems, inverse problems have no strict mathematical definition.

In general, they can be described as the task of recovering a part of the data of a corresponding direct (well-posed) problem from information about its solution. Inverse problems were first encountered in practice and are mostly ill-posed.

This book presents the theory of inverse spectral and scattering problems and of many other inverse problems for differential equations in an essentially self-contained way.

An outline of the theory of ill-posed problems is given, because inverse problems are often ill-posed. There are many novel features in this book.

We study optimal boundary control problems for the two-dimensional Navier--Stokes equations in an unbounded domain. Control is effected through the Dirichlet boundary condition and is sought in a s. Multidimensional inverse problems for differential equations / by: Inverse and ill-posed problems theory and applications / by: Inverse problems and high-dimensional estimation Stats in the Château Summer School, August September 4, / Published: ().New material is added to reflect recent progress in theory of inverse problems.

This book is intended for mathematicians working with partial differential equations and their applications, and physicists, geophysicists and engineers involved with experiments in nondestructive evaluation, seismic exploration, remote sensing and tomography.In this paper, we consider a two-dimensional (2D) time-fractional inverse diffusion problem which is severely ill-posed; i.e., the solution (if it exists) does not depend continuously on the data.

A modified kernel method is presented for approximating the solution of this problem, and the convergence estimates are obtained based on both a priori choice and a posteriori choice of.