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Moving Interfaces and Quasilinear Parabolic Evolution Equations / by Jan Prüss, Gieri Simonett
(Monographs in Mathematics. ISSN:22964886 ; 105)
版 | 1st ed. 2016. |
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出版者 | Cham : Springer International Publishing : Imprint: Birkhäuser |
出版年 | 2016 |
本文言語 | 英語 |
大きさ | XIX, 609 p. 7 illus : online resource |
著者標目 | *Prüss, Jan author Simonett, Gieri author SpringerLink (Online service) |
件 名 | LCSH:Differential equations LCSH:Mathematical physics LCSH:Functional analysis FREE:Differential Equations FREE:Mathematical Methods in Physics FREE:Functional Analysis |
一般注記 | Preface -- Basic Notations -- General References -- Part I Background -- 1Problems and Strategies -- 2.Tools from Differential Geometry -- Part II Abstract Theory -- 3Operator Theory and Semigroups -- 4.Vector-Valued Harmonic Analysis -- 5.Quasilinear Parabolic Evolution Equations -- Part III Linear Theory -- 6.Elliptic and Parabolic Problems -- 7.Generalized Stokes Problems -- 8.Two-Phase Stokes Problems -- Part IV Nonlinear Problems -- 9.Local Well-Posedness and Regularity -- 10.Linear Stability of Equilibria -- 11.Qualitative Behaviour of the Semiows -- 12.Further Parabolic Evolution Problems -- Biographical Comments -- Outlook and Future Challenges -- References -- List of Figures -- List of Symbols -- Subject Index In this monograph, the authors develop a comprehensive approach for the mathematical analysis of a wide array of problems involving moving interfaces. It includes an in-depth study of abstract quasilinear parabolic evolution equations, elliptic and parabolic boundary value problems, transmission problems, one- and two-phase Stokes problems, and the equations of incompressible viscous one- and two-phase fluid flows. The theory of maximal regularity, an essential element, is also fully developed. The authors present a modern approach based on powerful tools in classical analysis, functional analysis, and vector-valued harmonic analysis. The theory is applied to problems in two-phase fluid dynamics and phase transitions, one-phase generalized Newtonian fluids, nematic liquid crystal flows, Maxwell-Stefan diffusion, and a variety of geometric evolution equations. The book also includes a discussion of the underlying physical and thermodynamic principles governing the equations offluid flows and phase transitions, and an exposition of the geometry of moving hypersurfaces HTTP:URL=https://doi.org/10.1007/978-3-319-27698-4 |
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電子ブック | オンライン | 電子ブック |
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Springer eBooks | 9783319276984 |
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EB00232152 |
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