Ill-posed boundary-value problems

著者

• Temirbolat, S. E.

書誌事項

Ill-posed boundary-value problems

S.E. Temirbolat

（Inverse and ill-posed problems series）

VSP, 2003

注記

Includes bibliographical references (p. [139]-144)

内容説明・目次

内容説明

01/07 This title is now available from Walter de Gruyter. Please see www.degruyter.com for more information. The term "ill-posed problems" used to mean problems with unstable solutions for which small errors in initial data lead to a significant error in the results. At present the theory itself has been sufficiently well developed. At the same time the topic is by no means exhausted. This study is an attempt at extending well-known facts to new classes of problems and at working out novel approaches to the solution of these problems. In particular, this monograph is devoted to the questions of (consistency) of ill-posed boundary-value problems for systems of various types of the first-order differential equations with constant coefficients and to the methods of their solution. The introductory chapter gives some facts of the theory of matrices and ordinary differential equations. The first chapter studies the well posedness of the problem for an arbitrary system of ordinary equations and the occurrence of ill-posed problems among them. In the second chapter a similar approach is applied to various kinds of parabolic systems and solution methods for ill-posed problems are given. The final chapter deals with he afore mentioned methods to study problems for hyperbolic-type equations. This monograph will be of value to researchers in the field of ill-posed problems for differential equations.

目次

Introduction Conditionally well-posed problems and related questions Problems and methods for their investigation Denotation and terms Some facts from the theory of matrices Canonical (normal) forms of matrices On solutions of systems of algebraic equations Relation between an arbitrary equation and a system of first-order ordinary differential equations. Green's matrix Chapter 1. Construction of ill-posed problems for a system of the first order ODE Correct problem statement for an arbitrary system of ODE Problem on the ray t > 0 Problem on the interval Problem statement. Analysis of boundary conditions Linearization algorithm Chapter 2. Parabolic problems Parabolic systems Boundary-value problems The first boundary-value problem Mixed problem of heat and mass exchange Chapter 3. Hyperbolic equations Hyperbolicity and mixed problems Two-dimensional acoustic problem Linearized plane problem of gas dynamics Biblography

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詳細情報

• NII書誌ID(NCID): BA65599360
• ISBN:
  • 9067643955
• 出版国コード: ne
• タイトル言語コード: eng
• 本文言語コード: eng
• 出版地: Utrecht
• ページ数/冊数: viii, 144 p.
• 大きさ: 25 cm
• 親書誌ID:
  • BA2420606X