| 书目名称 | General Parabolic Mixed Order Systems in Lp and Applications |
| 编辑 | Robert Denk,Mario Kaip |
| 视频video | |
| 概述 | General approach to non-standard parabolic equations and systems.Unified treatment in several types of non-integer Lp-Sobolev spaces.Applicable to a large class of equations, e.g. to free boundary val |
| 丛书名称 | Operator Theory: Advances and Applications |
| 图书封面 |  |
| 描述 | In 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 .Lp-Lq.-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 .Lp.-Sobolev spaces as Besov spaces, Bessel potential spaces, and Triebel–Lizorkin spaces. The last-mentioned class appears in a natural way as traces of .Lp-Lq.-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 .Lp-Lq. two-phase Stefan problem with Gibbs–Thomson correction. |
| 出版日期 | Book 2013 |
| 关键词 | Newton-polygon; Triebel-Lizorkin spaces; free boundary problems; mixed order systems; parabolic differen |
| 版次 | 1 |
| doi | https://doi.org/10.1007/978-3-319-02000-6 |
| isbn_softcover | 978-3-319-37592-2 |
| isbn_ebook | 978-3-319-02000-6Series ISSN 0255-0156 Series E-ISSN 2296-4878 |
| issn_series | 0255-0156 |
| copyright | Springer International Publishing Switzerland 2013 |
发表于 2025-3-21 19:47:51
