{"product_id":"methods-for-solving-incorrectly-posed-problems-paperback","title":"Methods for Solving Incorrectly Posed Problems - Paperback","description":"\u003cp\u003eby \u003cb\u003eA. B. Aries\u003c\/b\u003e (Translator), \u003cb\u003eZ. Nashed\u003c\/b\u003e (Editor), \u003cb\u003eV. a. Morozov\u003c\/b\u003e (Author)\u003c\/p\u003e\u003cp\u003eSome 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.\u003c\/p\u003e\u003cdiv\u003e\n\u003cstrong\u003eNumber of Pages:\u003c\/strong\u003e 257\u003c\/div\u003e\u003cdiv\u003e\n\u003cstrong\u003eDimensions:\u003c\/strong\u003e 0.59 x 9.21 x 6.14 IN\u003c\/div\u003e\u003cdiv\u003e\n\u003cstrong\u003eIllustrated:\u003c\/strong\u003e Yes\u003c\/div\u003e\u003cdiv\u003e\n\u003cstrong\u003ePublication Date:\u003c\/strong\u003e November 20, 1984\u003c\/div\u003e","brand":"Books by splitShops","offers":[{"title":"Default Title","offer_id":42736842211391,"sku":"9780387960593","price":106.9,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0105\/8226\/1823\/files\/c03418a8e110737061033963d3eb0d93.webp?v=1765148041","url":"https:\/\/dhlswag.com\/products\/methods-for-solving-incorrectly-posed-problems-paperback","provider":"BBB","version":"1.0","type":"link"}