Inequalities in Mechanics and Physics
G. DuvantJ. L. Lions
Broschiertes Buch

Inequalities in Mechanics and Physics

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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, to, -a - du = g du = -a z + -a z + -a z t Xl X X3 z l g a given function, with boundary condit...