{"product_id":"general-parabolic-mixed-order-systems-in-lp-and-applications-hardcover-1","title":"General Parabolic Mixed Order Systems in LP and Applications - Hardcover","description":"\u003cdiv\u003e\u003cp style=\"text-align: right;\"\u003e\u003ca href=\"https:\/\/reportcopyrightinfringement.com\/\" target=\"_blank\" rel=\"nofollow\"\u003e\u003cb\u003eReport copyright infringement\u003c\/b\u003e\u003c\/a\u003e\u003c\/p\u003e\u003c\/div\u003e\u003cp\u003eby \u003cb\u003eRobert Denk\u003c\/b\u003e (Author), \u003cb\u003eMario Kaip\u003c\/b\u003e (Author)\u003c\/p\u003e\u003cp\u003eIn this text, a theory for general linear parabolic partial differential equations is established which covers equations with inhomogeneous symbol structure as well as mixed-order systems. Typical applications include several variants of the Stokes system and free boundary value problems. We show well-posedness in \u003ci\u003eLp-Lq\u003c\/i\u003e-Sobolev spaces in time and space for the linear problems (i.e., maximal regularity) which is the key step for the treatment of nonlinear problems. The theory is based on the concept of the Newton polygon and can cover equations which are not accessible by standard methods as, e.g., semigroup theory. Results are obtained in different types of non-integer \u003ci\u003eLp\u003c\/i\u003e-Sobolev spaces as Besov spaces, Bessel potential spaces, and Triebel-Lizorkin spaces. The last-mentioned class appears in a natural way as traces of \u003ci\u003eLp-Lq\u003c\/i\u003e-Sobolev spaces. We also present a selection of applications in the whole space and on half-spaces. Among others, we prove well-posedness of the linearizations of the generalized thermoelastic plate equation, the two-phase Navier-Stokes equations with Boussinesq-Scriven surface, and the \u003ci\u003eLp-Lq\u003c\/i\u003e two-phase Stefan problem with Gibbs-Thomson correction.​\u003c\/p\u003e\u003ch3\u003eBack Jacket\u003c\/h3\u003e\u003cp\u003eIn this text, a theory for general linear parabolic partial differential equations is established, which covers equations with inhomogeneous symbol structure as well as mixed order systems. Typical applications include several variants of the Stokes system and free boundary value problems. We show well-posedness in \u003ci\u003eLp-Lq\u003c\/i\u003e-Sobolev spaces in time and space for the linear problems (i.e., maximal regularity), which is the key step for the treatment of nonlinear problems. The theory is based on the concept of the Newton polygon and can cover equations that are not accessible by standard methods as, e.g., semigroup theory. Results are obtained in different types of non-integer \u003ci\u003eLp\u003c\/i\u003e-Sobolev spaces as Besov spaces, Bessel potential spaces, and Triebel-Lizorkin spaces. The latter class appears in a natural way as traces of \u003ci\u003eLp-Lq\u003c\/i\u003e-Sobolev spaces. We also present a selection of applications in the whole space and on half-spaces. Among others, we prove well-posedness of the linearizations of the generalized thermoelastic plate equation, the two-phase Navier-Stokes equations with Boussinesq-Scriven surface, and the \u003ci\u003eLp-Lq\u003c\/i\u003e two-phase Stefan problem with Gibbs-Thomson correction.\u003c\/p\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003eNumber of Pages:\u003c\/strong\u003e 250\u003c\/div\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003eDimensions:\u003c\/strong\u003e 0.63 x 9.21 x 6.14 IN\u003c\/div\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003eIllustrated:\u003c\/strong\u003e Yes\u003c\/div\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003ePublication Date:\u003c\/strong\u003e December 10, 2013\u003c\/div\u003e\n            ","brand":"BooksCloud","offers":[{"title":"Default Title","offer_id":53801503293747,"sku":"9783319019994","price":96.08,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0300\/5595\/6612\/files\/zvPkoOsZqA9783319019994_7f516639-25f0-4a85-8e36-cbbd201c5743.webp?v=1785968937","url":"https:\/\/www.vysn.com\/en-ca\/products\/general-parabolic-mixed-order-systems-in-lp-and-applications-hardcover-1","provider":"VYSN","version":"1.0","type":"link"}