{"product_id":"9780387960593","title":"Methods for Solving Incorrectly Posed Problems","description":"\u003ch1\u003eMethods for Solving Incorrectly Posed Problems\u003c\/h1\u003e \u003ch2\u003eMorozov, V.A.; Nashed, Z.; Aries, A.B.\u003c\/h2\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 \u003ch3\u003eDetails\u003c\/h3\u003e \u003cp\u003ePublished by: Springer\u003c\/p\u003e \u003cp\u003ePublication Date: 1984-11-20\u003c\/p\u003e \u003cp\u003eFormat: Paperback\u003c\/p\u003e \u003cp\u003eISBN-13: 9780387960593\u003c\/p\u003e \u003cp\u003eDOI: 10.1007\/978-1-4612-5280-1\u003c\/p\u003e \u003cp\u003eDimensions: 235cm x155cm\u003c\/p\u003e \u003cp\u003ePages: 257\u003c\/p\u003e ","brand":"Springer New York","offers":[{"title":"Default Title","offer_id":44422531874956,"sku":"9780387960593","price":49.49,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9780387960593.jpg?v=1775789631","url":"https:\/\/lateknightbooks.com\/products\/9780387960593","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}