Inequalities in Mechanics and Physics (Paperback, Softcover reprint of the original 1st ed. 1976)

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, to => 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.

General

Imprint:	Springer-Verlag
Country of origin:	Germany
Series:	Grundlehren der mathematischen Wissenschaften, 219
Release date:	November 2011
First published:	1976
Authors:	G Duvant
Translators:	C. W. John
Authors:	J.L. Lions
Dimensions:	244 x 170 x 21mm (L x W x T)
Format:	Paperback
Pages:	400
Edition:	Softcover reprint of the original 1st ed. 1976
ISBN-13:	978-3-642-66167-9
Categories:	Books > Science & Mathematics > Mathematics > General
LSN:	3-642-66167-X
Barcode:	9783642661679

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