Methods for Solving Incorrectly Posed Problems

Language: English

Published by Springer, Copernicus Nov 1984, 1984

0387960597 / 9780387960593

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This item is printed on demand - Print on Demand Titel. Neuware -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.Springer-Verlag KG, Sachsenplatz 4-6, 1201 Wien 280 pp. Englisch.

Seller Inventory # 9780387960593

Title
Methods for Solving Incorrectly Posed Problems
Author
V. A. Morozov
Publisher
Springer, Copernicus Nov 1984
Publication year
1984
Condition
Neu
Binding
Taschenbuch
Language
English
ISBN 10
0387960597
ISBN 13
9780387960593
Item weight
429 grams
Dimensions
235x155x16 mm

buchversandmimpf2000

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