Variational Problems with Concentration

Martin F. Bach

ISBN 10: 3034897294 / ISBN 13: 9783034897297

Published by Birkhäuser, 2012

Variational Problems with Concentration | Martin F. Bach | Taschenbuch | Progress in Nonlinear Differential Equations and Their Applications | viii | Englisch | 2012 | Birkhäuser | EAN 9783034897297 | Verantwortliche Person für die EU: Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, 14197 Berlin, juergen[dot]hartmann[at]springer[dot]com | Anbieter: preigu. Seller Inventory # 105706206

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.

Review:

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

--Zentralblatt Math

Bibliographic Details

Title: Variational Problems with Concentration
Publisher: Birkhäuser
Publication Date: 2012
Binding: Taschenbuch
Condition: Neu