Methods for Solving Incorrectly Posed Problems.

Morozov, V. A.:

ISBN 10: 3540960597 / ISBN 13: 9783540960591

Published by Springer Berlin, 1984

About this Item

xviii, 257 Seiten Einband etwas berieben, Bibl.Ex., innen guter und sauberer Zustand 9783540960591 Sprache: Englisch Gewicht in Gramm: 382.

Seller Inventory # 169514

Bibliographic Details

• Title: Methods for Solving Incorrectly Posed Problems.
• Publisher: Springer Berlin
• Publication Date: 1984
• Language: English
• ISBN 10: 3540960597
• ISBN 13: 9783540960591
• Binding: 8° , Softcover/Paperback
• Edition: 1.Auflage,.
• Weight: 382 grams
• Seller catalogs:
  • Mathematik

About this title

Synopsis

Some problems of mathematical physics and analysis can be formulated as the problem of solving the equation f F, (1) Au = f, where DA C U + F is an operator with a non-empty domain of definition D, in a metric space U, with range in a metric space F. The metrics A on U and F will be denoted by P and P ' respectively. Relative u F to the twin spaces U and F, J. Hadamard P-06] gave the following defini tion of the problem (1) is said to be well-posed (correct, properly posed) if the following conditions are (1) The range of the value Q of the operator A coincides with A F ("sol vabi li ty" condition); (2) The equality AU = AU for any u, u DA implies the I 2 l 2 equality u = u ("uniqueness" condition); l 2 (3) The inverse operator A-I is continuous on F ("stability" condition). Any reasonable mathematical formulation of a physical problem requires that conditions (1)-(3) be satisfied. That is why Hadamard postulated that any "ill-posed" (improperly posed) problem, that is to say, one which does not satisfy conditions (1)-(3), is non-physical. Hadamard also gave the now classical example of an ill-posed problem, namely, the Cauchy problem for the Laplace equation."

Language Notes

Text: English (translation)
Original Language: Russian