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Titlebook: General Parabolic Mixed Order Systems in Lp and Applications; Robert Denk,Mario Kaip Book 2013 Springer International Publishing Switzerla

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發(fā)表于 2025-3-21 19:47:51 | 只看該作者 |倒序瀏覽 |閱讀模式
書目名稱General Parabolic Mixed Order Systems in Lp and Applications
編輯Robert Denk,Mario Kaip
視頻videohttp://file.papertrans.cn/383/382084/382084.mp4
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
叢書名稱Operator Theory: Advances and Applications
圖書封面Titlebook: General Parabolic Mixed Order Systems in Lp and Applications;  Robert Denk,Mario Kaip Book 2013 Springer International Publishing Switzerla
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
關(guān)鍵詞Newton-polygon; Triebel-Lizorkin spaces; free boundary problems; mixed order systems; parabolic differen
版次1
doihttps://doi.org/10.1007/978-3-319-02000-6
isbn_softcover978-3-319-37592-2
isbn_ebook978-3-319-02000-6Series ISSN 0255-0156 Series E-ISSN 2296-4878
issn_series 0255-0156
copyrightSpringer International Publishing Switzerland 2013
The information of publication is updating

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沙發(fā)
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板凳
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地板
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5#
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https://doi.org/10.1007/978-1-349-23219-2ic and parabolic theory, these symbols are (quasi-)homogeneous. In this case, the condition that the symbol does not vanish automatically implies uniform estimates on its inverse. In several classes of applications, however, the symbol does not have a quasihomogeneous structure. During the 1990‘s, t
6#
發(fā)表于 2025-3-22 16:14:56 | 只看該作者
https://doi.org/10.1007/978-3-030-20918-6and Corollary 3.44. The applications split into two subgroups of parabolic partial differential equations. In the first part we consider problems on the whole space and in the second part we consider boundary value problems. This seems to be one of the first works which treat parabolic problems on t
7#
發(fā)表于 2025-3-22 18:12:06 | 只看該作者
Robert Denk,Mario KaipGeneral 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
8#
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9#
發(fā)表于 2025-3-23 01:55:48 | 只看該作者
New Media Enterprise in the Age of SuspicionIn this chapter we want to generalize the results of Section 2.3 on mixed-order systems to the scale of Triebel-Lizorkin spaces. Triebel-Lizorkin spaces naturally appear in parabolic ..-..-theory as the trace spaces of the solution.
10#
發(fā)表于 2025-3-23 07:01:49 | 只看該作者
The joint time-space ,,-calculus,One of the most successful approaches in the theory of partial di_erential equations is based on the Fourier transform and the symbols of di_erential operators and their inverses. The Fourier transform maps di_erentiation into multiplication by the covariable and thus directly leads to a representation of the inverse (i.e., solution) operator.
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