{"product_id":"9783642661679","title":"Grundlehren der mathematischen Wissenschaften","description":"\u003ch1\u003eGrundlehren der mathematischen Wissenschaften\u003c\/h1\u003e \u003ch2\u003eDuvant, G.; John, C. W.; Lions, J. L.\u003c\/h2\u003e \u003cp\u003e1. We begin by giving a simple example of a partial differential inequality that occurs in an elementary physics problem. We consider a fluid with pressure u(x, t) at the point x at the instant t that 3 occupies a region Q oflR bounded by a membrane r of negligible thickness that, however, is semi-permeable, i. e., a membrane that permits the fluid to enter Q freely but that prevents all outflow of fluid. One can prove then (cf. the details in Chapter 1, Section 2.2.1) that au (aZu azu aZu) (1) in Q, t\u0026gt;o, -a - du = g du = -a z + -a z + -a z t Xl X X3 z l g a given function, with boundary conditions in the form of inequalities u(X,t»o =\u0026gt; au(x,t)\/an=O, XEr, (2) u(x,t)=o =\u0026gt; au(x,t)\/an?:O, XEr, to which is added the initial condition (3) u(x,O)=uo(x). We note that conditions (2) are non linear; they imply that, at each fixed instant t, there exist on r two regions r~ and n where u(x, t) =0 and au (x, t)\/an = 0, respectively. These regions are not prescribed; thus we deal with a \"free boundary\" problem.\u003c\/p\u003e \u003ch3\u003eDetails\u003c\/h3\u003e \u003cp\u003ePublished by: Springer\u003c\/p\u003e \u003cp\u003ePublication Date: 2011-11-15\u003c\/p\u003e \u003cp\u003eFormat: Paperback\u003c\/p\u003e \u003cp\u003eISBN-13: 9783642661679\u003c\/p\u003e \u003cp\u003eDOI: 10.1007\/978-3-642-66165-5\u003c\/p\u003e \u003cp\u003eDimensions: 244cm x170cm\u003c\/p\u003e \u003cp\u003ePages: 400\u003c\/p\u003e ","brand":"Springer Berlin Heidelberg","offers":[{"title":"Default Title","offer_id":44450508144780,"sku":"9783642661679","price":116.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9783642661679.jpg?v=1775731697","url":"https:\/\/lateknightbooks.com\/products\/9783642661679","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}