Variational Problems with Concentration (Progress in Nonlinear Differential Equations and Their Applications, 36) - Hardcover

Bach, Martin F.

Hardcover

ISBN 10: 3764361360 ISBN 13: 9783764361365

Publisher: Birkhäuser, 1999

Synopsis

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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Review

"This material is very rich, because various alternatives are possible. The book provides a good systematic overview of this difficult topic."

--Zentralblatt Math

Edition details

• Publisher: Birkhäuser
• Publication date: 1999
• Language: English
• ISBN 10: 3764361360
• ISBN 13: 9783764361365
• Binding: Hardcover
• Number of pages: 176