{"product_id":"9783764361365","title":"Progress in Nonlinear Differential Equations and Their Applications","description":"\u003ch1\u003eProgress in Nonlinear Differential Equations and Their Applications\u003c\/h1\u003e \u003ch2\u003eBach, Martin F.\u003c\/h2\u003e \u003cp\u003eTo 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.\u003c\/p\u003e \u003ch3\u003eDetails\u003c\/h3\u003e \u003cp\u003ePublished by: Birkhäuser\u003c\/p\u003e \u003cp\u003ePublication Date: 1999-07-01\u003c\/p\u003e \u003cp\u003eFormat: Hardcover\u003c\/p\u003e \u003cp\u003eISBN-13: 9783764361365\u003c\/p\u003e \u003cp\u003eDOI: 10.1007\/978-3-0348-8687-1\u003c\/p\u003e \u003cp\u003eDimensions: 235cm x155cm\u003c\/p\u003e \u003cp\u003ePages: 163\u003c\/p\u003e ","brand":"Birkhäuser Basel","offers":[{"title":"Default Title","offer_id":45378501247116,"sku":"9783764361365","price":107.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9783764361365.jpg?v=1775703777","url":"https:\/\/fh90cf-fv.myshopify.com\/products\/9783764361365","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}