Generalized Solutions of First Order PDEs is popular PDF and ePub book, written by Andrei I. Subbotin in 2013-06-29, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, Generalized Solutions of First Order PDEs can be Read Online from any device for your convenience.
Generalized Solutions of First Order PDEs Book PDF Summary
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].
Detail Book of Generalized Solutions of First Order PDEs PDF
- Author : Andrei I. Subbotin
- Release : 29 June 2013
- Publisher : Springer Science & Business Media
- ISBN : 9781461208471
- Genre : Mathematics
- Total Page : 324 pages
- Language : English
- PDF File Size : 14,6 Mb
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