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 ...
Read More
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.
Read Less
Add this copy of Methods for Solving Incorrectly Posed Problems to cart. $29.32, very good condition, Sold by ThriftBooks-Dallas rated 5.0 out of 5 stars, ships from Dallas, TX, UNITED STATES, published 1984 by Springer.
Add this copy of Methods for Solving Incorrectly Posed Problems to cart. $41.21, very good condition, Sold by Zubal Books rated 4.0 out of 5 stars, ships from Cleveland, OH, UNITED STATES, published 1984 by Springer.
Choose your shipping method in Checkout. Costs may vary based on destination.
Seller's Description:
*Price HAS BEEN REDUCED by 10% until Monday, May 5 (weekend SALE item)* First edition, first printing, 257 pp., Paperback, a TINY bit of discoloration to fore edge else fine. -If you are reading this, this item is actually (physically) in our stock and ready for shipment once ordered. We are not bookjackers. Buyer is responsible for any additional duties, taxes, or fees required by recipient's country.
Add this copy of Methods for Solving Incorrectly Posed Problems to cart. $51.65, new condition, Sold by Ingram Customer Returns Center rated 5.0 out of 5 stars, ships from NV, USA, published 1984 by Springer.
Add this copy of Methods for Solving Incorrectly Posed Problems to cart. $65.79, good condition, Sold by Bonita rated 4.0 out of 5 stars, ships from Santa Clarita, CA, UNITED STATES, published 1984 by Springer.
