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Titlebook: Inequalities in Mechanics and Physics; Georges Duvaut,Jacques Louis Lions Book 1976 Springer-Verlag Berlin Heidelberg 1976 Finite.Ungleich

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发表于 2025-3-21 18:49:25 | 显示全部楼层 |阅读模式
书目名称Inequalities in Mechanics and Physics
编辑Georges Duvaut,Jacques Louis Lions
视频videohttp://file.papertrans.cn/465/464396/464396.mp4
丛书名称Grundlehren der mathematischen Wissenschaften
图书封面Titlebook: Inequalities in Mechanics and Physics;  Georges Duvaut,Jacques Louis Lions Book 1976 Springer-Verlag Berlin Heidelberg 1976 Finite.Ungleich
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
doihttps://doi.org/10.1007/978-3-642-66165-5
isbn_softcover978-3-642-66167-9
isbn_ebook978-3-642-66165-5Series ISSN 0072-7830 Series E-ISSN 2196-9701
issn_series 0072-7830
copyrightSpringer-Verlag Berlin Heidelberg 1976
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发表于 2025-3-21 20:14:51 | 显示全部楼层
,Maxwell’s Equations. Antenna Problems,utions in Sections 4–6. This theory is indispensable for the subsequent treatment of Maxwell’s equations in a polarizable medium. Section 3 is a presentation of the physical problems under consideration.
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Book 1976ssure 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 Ch
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发表于 2025-3-22 11:47:59 | 显示全部楼层
,Maxwell’s Equations. Antenna Problems, are coupled, with the mechanics of Bingham fluids yielding the magnetodynamics of Bingham fluids. This second possibility is treated in Duvaut-Lions [7]. The present chapter is devoted to unilateral problems connected with Maxwell’s equations. Since we cannot refer to a unified exposition of the cl
发表于 2025-3-22 16:47:18 | 显示全部楼层
Georges Duvaut,Jacques Louis Lionsunite and divide us. Human affairs impinge inevitably on questions of identity and belonging that hinge on and sometimes challenge state frontiers, national membership, civic ties, the bounds of religious and ethnic collectivities, and the limits of moral community. Any given day is likely to bring
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Book 1976=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.
发表于 2025-3-23 04:47:24 | 显示全部楼层
发表于 2025-3-23 07:48:36 | 显示全部楼层
Georges Duvaut,Jacques Louis Lions characteristic concerns have hitherto gone entirely unaddressed. To the contrary, the issue has been implicitly addressed in some of the more innovative recent work in political theory and social ethics. In this chapter, I explore four diverse lines of inquiry into justice and the ethics of boundar
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