Discontinuous Initial Value Problems And Asymptotic Expansion of Steady State So
Discontinuous Initial Value Problems And Asymptotic Expansion of Steady State So
Robert M Lewis
The book Discontinuous Initial Value Problems And Asymptotic Expansion of Steady State So was written by author Robert M Lewis Here you can read free online of Discontinuous Initial Value Problems And Asymptotic Expansion of Steady State So book, rate and share your impressions in comments. If you don't know what to write, just answer the question: Why is Discontinuous Initial Value Problems And Asymptotic Expansion of Steady State So a good or bad book?
What reading level is Discontinuous Initial Value Problems And Asymptotic Expansion of Steady State So book?
To quickly assess the difficulty of the text, read a short excerpt:
In Section 6 we will show that these hypersurfaces can never have a tangent plane parallel to the t-axis, so they can be defined by equations of the form t « T^°'(x), With this information, the asymptotic expansion of the integral (122) is obtained simply by repeated integrations by parts. At each step we obtain contributions from the lower end point of the integral and from the dis- continuities of u and its derivatives. We shall assume that the discontinuities - 68 - of u and its derivatives ...with respect to t all occur on a finite number of hyper- surfaces t - f (x)j a - l, . , . , p. We write ^(1) ^(2) 00 (125) v(x) - [' * [ * ••• + u(t, x)e^*dt . Integrating by parts (126) v(x) . - ^%S) - 2: ?-, _ \_. T-\ \ *■■■*[ • r-0 (lo)) a r"0 l_t_l « If g(x) is sufficiently smooth, we know from Part I that u will be smooth and the terms involving [u ]*^ will vanish. Now compare (130) with (10), We see that V « y is indeed an asymptotic expansion to M terms of v. In the general case, where g and its derivatives are discontinuous across p, we must determine the functions (-1) ) [u 1'^ which appear in (130), We shall identify them with the terms z^°'^ "^ in the formal expansion (see (3I4) and (13)).
You can download books for free in various formats, such as epub, pdf, azw, mobi, txt and others on book networks site. Additionally, the entire text is available for online reading through our e-reader. Our site is not responsible for the performance of third-party products (sites).
User Reviews: