{"product_id":"methods-for-solving-incorrectly-posed-problems-9780387960593","title":"Methods for Solving Incorrectly Posed Problems","description":"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.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eAuthor:\u003c\/b\u003e A. B. Aries, V. a. Morozov\u003cbr\u003e\u003cb\u003ePublisher:\u003c\/b\u003e Springer\u003cbr\u003e\u003cb\u003ePublished:\u003c\/b\u003e 11\/20\/1984\u003cbr\u003e\u003cb\u003ePages:\u003c\/b\u003e 257\u003cbr\u003e\u003cb\u003eBinding Type:\u003c\/b\u003e Paperback\u003cbr\u003e\u003cb\u003eWeight:\u003c\/b\u003e 0.87lbs\u003cbr\u003e\u003cb\u003eSize:\u003c\/b\u003e 9.21h x 6.14w x 0.59d\u003cbr\u003e\u003cb\u003eISBN:\u003c\/b\u003e 9780387960593","brand":"Springer","offers":[{"title":"Paperback","offer_id":41142624387187,"sku":"9.78039E+12","price":93.38,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0555\/9255\/0515\/products\/img_52bdbcb6-48e3-4995-b465-cfd9b3d288d7.jpg?v=1701876208","url":"https:\/\/bookstorenmore.com\/products\/methods-for-solving-incorrectly-posed-problems-9780387960593","provider":"Bookstore N More","version":"1.0","type":"link"}