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# Inequalities in Mechanics and Physics

## af G. Duvant, J. L. Lions & G. Duvant

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• Forventet levering 28-02-2019
• 18%
Format:
Bog, hæftet
Udgivelsesdato:
01-11-2011
Sprog:
Engelsk
Sidetal:
420
Læsernes anmeldelser
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1. Beskrivelse

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.

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E-bog, PDF

2. Yderligere info
ISBN13:
9783642661679
Vægt:
667 g
Dybde:
22 mm
Bredde:
170 mm
Højde:
244 mm
Forlag:
Springer
Format:
Hæftet
3. Anmeldelser

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