{"product_id":"generalized-solutions-of-first-order-andrei-i-subbotin-9780817637408","title":"Generalized Solutions of First Order Pdes: The Dynamical Optimization Perspective","description":"Hamilton-Jacobi equations and other types of partial differential equa- tions of the first order are dealt with in many branches of mathematics, mechanics, and physics. These equations are usually nonlinear, and func- tions vital for the considered problems are not smooth enough to satisfy these equations in the classical sense. An example of such a situation can be provided by the value function of a differential game or an optimal control problem. It is known that at the points of differentiability this function satisfies the corresponding Hamilton-Jacobi-Isaacs-Bellman equation. On the other hand, it is well known that the value function is as a rule not everywhere differentiable and therefore is not a classical global solution. Thus in this case, as in many others where first-order PDE's are used, there arises necessity to introduce a notion of generalized solution and to develop theory and methods for constructing these solutions. In the 50s-70s, problems that involve nonsmooth solutions of first- order PDE's were considered by Bakhvalov, Evans, Fleming, Gel'fand, Godunov, Hopf, Kuznetzov, Ladyzhenskaya, Lax, Oleinik, Rozhdestven- ski1, Samarskii, Tikhonov, and other mathematicians. Among the inves- tigations of this period we should mention the results of S.N. Kruzhkov, which were obtained for Hamilton-Jacobi equation with convex Hamilto- nian. A review of the investigations of this period is beyond the limits of the present book. A sufficiently complete bibliography can be found in  58, 126, 128, 141].\u003cbr\u003e\u003cbr\u003e\u003cb\u003eAuthor:\u003c\/b\u003e Andrei I. Subbotin\u003cbr\u003e\u003cb\u003eISBN-10:\u003c\/b\u003e 0817637400\u003cbr\u003e\u003cb\u003eISBN-13:\u003c\/b\u003e 9780817637408\u003cbr\u003e\u003cb\u003ePublisher:\u003c\/b\u003e Birkhauser\u003cbr\u003e\u003cb\u003eLanguage:\u003c\/b\u003e English\u003cbr\u003e\u003cb\u003ePublished:\u003c\/b\u003e 12\/22\/1994\u003cbr\u003e\u003cb\u003ePages:\u003c\/b\u003e 314\u003cbr\u003e\u003cb\u003eFormat:\u003c\/b\u003e Hardcover\u003cbr\u003e\u003cb\u003eWeight:\u003c\/b\u003e 1.44lbs\u003cbr\u003e\u003cb\u003eSize:\u003c\/b\u003e 9.50h x 6.29w x 0.78d","brand":"Andrei I. Subbotin","offers":[{"title":"Hardcover","offer_id":44059861680383,"sku":"9780817637408","price":109.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0662\/2982\/9887\/files\/img_63e13b5f-b939-4f24-a605-c225c48d7842.jpg?v=1685060750","url":"https:\/\/www.whiterainbookhouse.com\/products\/generalized-solutions-of-first-order-andrei-i-subbotin-9780817637408","provider":"WR Book House","version":"1.0","type":"link"}