Methods for Solving Incorrectly Posed Problems - Couverture souple

Morozov, V. A.

Couverture souple

ISBN 10 : 0387960597 ISBN 13 : 9780387960593

Editeur : Springer New York, 1984

Synopsis

Some problems of mathematical physics and analysis can be formulated as the problem of solving the equation f F, (1) Au = f, where A: 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 correctness: the problem (1) is said to be well-posed (correct, properly posed) if the following conditions are satisfied: (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.

Détails de l'édition

• Éditeur: Springer New York
• Date d'édition: 1984
• Langue: anglais
• ISBN 10: 0387960597
• ISBN 13: 9780387960593
• Reliure: Broché
• Nombre de pages: 280
• Coordonnées du fabricant: non disponible
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