Inequalities in Mechanics and Physics
No Customer Reviews
Select Format
Select Condition 
Book Overview
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.
Format:Paperback
Language:English
ISBN:364266167X
ISBN13:9783642661679
Release Date:November 2011
Publisher:Springer
Length:400 Pages
Weight:1.47 lbs.
Dimensions:0.9" x 6.7" x 9.6"
Customer Reviews
0 rating
Copyright © 2025 Thriftbooks.com
Terms of Use | Privacy Policy | Do Not Sell/Share My Personal Information | Cookie Policy | Cookie Preferences | Accessibility Statement
ThriftBooks ® and the ThriftBooks ® logo are registered trademarks of Thrift Books Global, LLC
ThriftBooks ® and the ThriftBooks ® logo are registered trademarks of Thrift Books Global, LLC
