{"product_id":"methods-for-solving-incorrectly-posed-problems-0387960597","title":"Methods for Solving Incorrectly Posed Problems","description":"\u003cp\u003e\u003cstrong\u003eISBN:\u003c\/strong\u003e 0387960597\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eAuthor:\u003c\/strong\u003e Morozov, V.A.\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eCondition:\u003c\/strong\u003e New\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","brand":"Mia Karts","offers":[{"title":"Default Title","offer_id":51824036380960,"sku":"NEW0387960597","price":60.26,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0980\/7426\/3840\/files\/51N2ALp06JL.jpg?v=1781206939","url":"https:\/\/miakarts.com\/products\/methods-for-solving-incorrectly-posed-problems-0387960597","provider":"Miakarts Books","version":"1.0","type":"link"}