General Parabolic Mixed Order Systems In Lp And Applications PDF Download
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| Author | : Robert Denk |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 254 |
| Release | : 2013-11-22 |
| Genre | : Mathematics |
| ISBN | : 3319020005 |
Download General Parabolic Mixed Order Systems in Lp and Applications Book in PDF, ePub and Kindle
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.
| Author | : Mario Kaip |
| Publisher | : |
| Total Pages | : 186 |
| Release | : 2012 |
| Genre | : |
| ISBN | : |
Download General Parabolic Mixed Order Systems in L[sub P] and Applications Book in PDF, ePub and Kindle
| Author | : Shigeaki Koike |
| Publisher | : Springer Nature |
| Total Pages | : 267 |
| Release | : 2021-04-16 |
| Genre | : Mathematics |
| ISBN | : 9813348224 |
Download Nonlinear Partial Differential Equations for Future Applications Book in PDF, ePub and Kindle
This volume features selected, original, and peer-reviewed papers on topics from a series of workshops on Nonlinear Partial Differential Equations for Future Applications that were held in 2017 at Tohoku University in Japan. The contributions address an abstract maximal regularity with applications to parabolic equations, stability, and bifurcation for viscous compressible Navier–Stokes equations, new estimates for a compressible Gross–Pitaevskii–Navier–Stokes system, singular limits for the Keller–Segel system in critical spaces, the dynamic programming principle for stochastic optimal control, two kinds of regularity machineries for elliptic obstacle problems, and new insight on topology of nodal sets of high-energy eigenfunctions of the Laplacian. This book aims to exhibit various theories and methods that appear in the study of nonlinear partial differential equations.
| Author | : Jan Prüss |
| Publisher | : Birkhäuser |
| Total Pages | : 618 |
| Release | : 2016-07-25 |
| Genre | : Mathematics |
| ISBN | : 3319276980 |
Download Moving Interfaces and Quasilinear Parabolic Evolution Equations Book in PDF, ePub and Kindle
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 of fluid flows and phase transitions, and an exposition of the geometry of moving hypersurfaces.
| Author | : Herbert Amann |
| Publisher | : Springer |
| Total Pages | : 462 |
| Release | : 2019-04-16 |
| Genre | : Mathematics |
| ISBN | : 3030117634 |
Download Linear and Quasilinear Parabolic Problems Book in PDF, ePub and Kindle
This volume discusses an in-depth theory of function spaces in an Euclidean setting, including several new features, not previously covered in the literature. In particular, it develops a unified theory of anisotropic Besov and Bessel potential spaces on Euclidean corners, with infinite-dimensional Banach spaces as targets. It especially highlights the most important subclasses of Besov spaces, namely Slobodeckii and Hölder spaces. In this case, no restrictions are imposed on the target spaces, except for reflexivity assumptions in duality results. In this general setting, the author proves sharp embedding, interpolation, and trace theorems, point-wise multiplier results, as well as Gagliardo-Nirenberg estimates and generalizations of Aubin-Lions compactness theorems. The results presented pave the way for new applications in situations where infinite-dimensional target spaces are relevant – in the realm of stochastic differential equations, for example.
| Author | : Tuomas Hytönen |
| Publisher | : Springer Nature |
| Total Pages | : 839 |
| Release | : 2024-01-08 |
| Genre | : Mathematics |
| ISBN | : 3031465989 |
Download Analysis in Banach Spaces Book in PDF, ePub and Kindle
This third volume of Analysis in Banach Spaces offers a systematic treatment of Banach space-valued singular integrals, Fourier transforms, and function spaces. It further develops and ramifies the theory of functional calculus from Volume II and describes applications of these new notions and tools to the problem of maximal regularity of evolution equations. The exposition provides a unified treatment of a large body of results, much of which has previously only been available in the form of research papers. Some of the more classical topics are presented in a novel way using modern techniques amenable to a vector-valued treatment. Thanks to its accessible style with complete and detailed proofs, this book will be an invaluable reference for researchers interested in functional analysis, harmonic analysis, and the operator-theoretic approach to deterministic and stochastic evolution equations.
| Author | : Yoshihiro Shibata |
| Publisher | : Springer |
| Total Pages | : 616 |
| Release | : 2016-12-01 |
| Genre | : Mathematics |
| ISBN | : 4431564578 |
Download Mathematical Fluid Dynamics, Present and Future Book in PDF, ePub and Kindle
This volume presents original papers ranging from an experimental study on cavitation jets to an up-to-date mathematical analysis of the Navier-Stokes equations for free boundary problems, reflecting topics featured at the International Conference on Mathematical Fluid Dynamics, Present and Future, held 11–14 November 2014 at Waseda University in Tokyo. The contributions address subjects in one- and two-phase fluid flows, including cavitation, liquid crystal flows, plasma flows, and blood flows. Written by internationally respected experts, these papers highlight the connections between mathematical, experimental, and computational fluid dynamics. The book is aimed at a wide readership in mathematics and engineering, including researchers and graduate students interested in mathematical fluid dynamics.
| Author | : Dung Le |
| Publisher | : Walter de Gruyter GmbH & Co KG |
| Total Pages | : 195 |
| Release | : 2018-11-05 |
| Genre | : Mathematics |
| ISBN | : 3110608766 |
Download Strongly Coupled Parabolic and Elliptic Systems Book in PDF, ePub and Kindle
Strongly coupled (or cross-diffusion) systems of parabolic and elliptic partial differential equations appear in many physical applications. This book presents a new approach to the solvability of general strongly coupled systems, a much more difficult problem in contrast to the scalar case, by unifying, elucidating and extending breakthrough results obtained by the author, and providing solutions to many open fundamental questions in the theory. Several examples in mathematical biology and ecology are also included. Contents Interpolation Gagliardo–Nirenberg inequalities The parabolic systems The elliptic systems Cross-diffusion systems of porous media type Nontrivial steady-state solutions The duality RBMO(μ)–H1(μ)| Some algebraic inequalities Partial regularity
| Author | : Pekka Neittaanmaki |
| Publisher | : CRC Press |
| Total Pages | : 432 |
| Release | : 1994-02-08 |
| Genre | : Mathematics |
| ISBN | : 9780824790813 |
Download Optimal Control of Nonlinear Parabolic Systems Book in PDF, ePub and Kindle
This book discusses theoretical approaches to the study of optimal control problems governed by non-linear evolutions - including semi-linear equations, variational inequalities and systems with phase transitions. It also provides algorithms for solving non-linear parabolic systems and multiphase Stefan-like systems.
| Author | : David Hoff |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 226 |
| Release | : 2020-11-18 |
| Genre | : Education |
| ISBN | : 1470461617 |
Download Linear and Quasilinear Parabolic Systems: Sobolev Space Theory Book in PDF, ePub and Kindle
This monograph presents a systematic theory of weak solutions in Hilbert-Sobolev spaces of initial-boundary value problems for parabolic systems of partial differential equations with general essential and natural boundary conditions and minimal hypotheses on coefficients. Applications to quasilinear systems are given, including local existence for large data, global existence near an attractor, the Leray and Hopf theorems for the Navier-Stokes equations and results concerning invariant regions. Supplementary material is provided, including a self-contained treatment of the calculus of Sobolev functions on the boundaries of Lipschitz domains and a thorough discussion of measurability considerations for elements of Bochner-Sobolev spaces. This book will be particularly useful both for researchers requiring accessible and broadly applicable formulations of standard results as well as for students preparing for research in applied analysis. Readers should be familiar with the basic facts of measure theory and functional analysis, including weak derivatives and Sobolev spaces. Prior work in partial differential equations is helpful but not required.
