Ill-Posed Boundary-Value Problems

Thismonograph extends well-known facts to new classes of problems andworks out novel approaches to the solution ofthese problems. It is devoted to the questions of ill-posed boundary-value problems for systems of various types of the first-order differential equations with constant coefficients and the methods for their solution.

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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.