书目名称 | Inequalities in Mechanics and Physics | 编辑 | Georges Duvaut,Jacques Louis Lions | 视频video | http://file.papertrans.cn/465/464396/464396.mp4 | 丛书名称 | Grundlehren der mathematischen Wissenschaften | 图书封面 |  | 描述 | 1. We begin by giving a simple example of a partial differential inequality that occurs in an elementary physics problem. We consider a fluid with pressure u(x, t) at the point x at the instant t that 3 occupies a region Q oflR bounded by a membrane r of negligible thickness that, however, is semi-permeable, i. e., a membrane that permits the fluid to enter Q freely but that prevents all outflow of fluid. One can prove then (cf. the details in Chapter 1, Section 2.2.1) that au (aZu azu aZu) (1) in Q, t>o, -a - du = g du = -a z + -a z + -a z t Xl X X3 z l g a given function, with boundary conditions in the form of inequalities u(X,t»o => au(x,t)/an=O, XEr, (2) u(x,t)=o => au(x,t)/an?:O, XEr, to which is added the initial condition (3) u(x,O)=uo(x). We note that conditions (2) are non linear; they imply that, at each fixed instant t, there exist on r two regions r~ and n where u(x, t) =0 and au (x, t)/an = 0, respectively. These regions are not prescribed; thus we deal with a "free boundary" problem. | 出版日期 | Book 1976 | 关键词 | Finite; Ungleichung; approximation; calculus; continuum mechanics; duality; elasticity; equation; function; m | 版次 | 1 | doi | https://doi.org/10.1007/978-3-642-66165-5 | isbn_softcover | 978-3-642-66167-9 | isbn_ebook | 978-3-642-66165-5Series ISSN 0072-7830 Series E-ISSN 2196-9701 | issn_series | 0072-7830 | copyright | Springer-Verlag Berlin Heidelberg 1976 |
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