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# Catalogue Display

## Inequalities in Mechanics and Physics

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Catalogue Information
Field name Details
Dewey Class 510
Title Inequalities in Mechanics and Physics ([EBook] /) / by Georges Duvaut, Jacques Louis Lions.
Author Duvaut, Georges
Added Personal Name Lions, Jacques-Louis author.
Publication Berlin, Heidelberg : : Springer Berlin Heidelberg, , 1976.
Physical Details XVI, 400 p. : online resource.
Series Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics 0072-7830 ; ; 219
ISBN 9783642661655
Summary Note 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.:
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Internet Site http://dx.doi.org/10.1007/978-3-642-66165-5