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Inequalities in Mechanics and Physics by G. Duvant

Inequalities in Mechanics and Physics

by G. Duvant
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Book cover type: Paperback
  • ISBN13: 9783642661679
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Springer
  • Publisher Imprint: Springer
  • Publication Date:
  • Pages: 400
  • Original Price: EUR 119.99
  • Language: English
  • Edition: Softcover Repri
  • Item Weight: 719 grams
  • BISAC Subject(s): General

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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