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Variational Problems with Concentration Softcover Repri Edition
Contributor(s): Bach, Martin F. (Author)

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 ISBN: 3034897294     ISBN-13: 9783034897297
Publisher: Birkhauser
OUR PRICE: $104.49  

Binding Type: Paperback - See All Available Formats & Editions
Published: November 2012
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Click for more in this series: Progress in Nonlinear Differential Equations and Their Appli
Additional Information
BISAC Categories:
- Mathematics | Differential Equations - Partial
- Medical
- Mathematics | Number Systems
Dewey: 515.353
Series: Progress in Nonlinear Differential Equations and Their Appli
Physical Information: 0.38" H x 6.14" W x 9.21" L (0.56 lbs) 163 pages
 
Descriptions, Reviews, Etc.
Publisher Description:
To start with we describe two applications of the theory to be developed in this monograph: Bernoulli's free-boundary problem and the plasma problem. Bernoulli's free-boundary problem This problem arises in electrostatics, fluid dynamics, optimal insulation, and electro chemistry. In electrostatic terms the task is to design an annular con- denser consisting of a prescribed conducting surface 80. and an unknown conduc- tor A such that the electric field 'Vu is constant in magnitude on the surface 8A of the second conductor (Figure 1.1). This leads to the following free-boundary problem for the electric potential u. - u 0 in 0. \A, u 0 on 80., u 1 on 8A, 8u Q on 8A. 811 The unknowns are the free boundary 8A and the potential u. In optimal in- sulation problems the domain 0. \ A represents the insulation layer. Given the exterior boundary 80. the problem is to design an insulating layer 0. \ A of given volume which minimizes the heat or current leakage from A to the environment ]R.n \ n. The heat leakage per unit time is the capacity of the set A with respect to n. Thus we seek to minimize the capacity among all sets A c 0. of equal volume.
 
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