Variational Problems with Concentration

By:

Martin F. Bach

Format:

Paperback / softback

Series:

Progress in Nonlinear Differential Equations and Their Applications

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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.

Release date NZ

July 1st, 1999

Author

Martin F. Bach

Audience

Professional & Vocational

Edition

Softcover reprint of the original 1st ed. 1999

Illustrations

VIII, 163 p.

Pages

163

Series

Progress in Nonlinear Differential Equations and Their Applications

Dimensions

155x235x9

ISBN-13

9783034897297

Product ID

21577703

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