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Linear and Quasilinear Parabolic Systems: Sobolev Space Theory

2020-11-18 Education
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Release : 2020-11-18
Genre : Education
Kind : eBook
Book Rating : 617/5 ( reviews)

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Book Synopsis Linear and Quasilinear Parabolic Systems: Sobolev Space Theory by : David Hoff

Download or read book Linear and Quasilinear Parabolic Systems: Sobolev Space Theory written by David Hoff. This book was released on 2020-11-18. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Linear and Quasilinear Parabolic Problems

2012-12-06 Mathematics
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Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 217/5 ( reviews)

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Book Synopsis Linear and Quasilinear Parabolic Problems by : Herbert Amann

Download or read book Linear and Quasilinear Parabolic Problems written by Herbert Amann. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: In this treatise we present the semigroup approach to quasilinear evolution equa of parabolic type that has been developed over the last ten years, approxi tions mately. It emphasizes the dynamic viewpoint and is sufficiently general and flexible to encompass a great variety of concrete systems of partial differential equations occurring in science, some of those being of rather 'nonstandard' type. In partic ular, to date it is the only general method that applies to noncoercive systems. Although we are interested in nonlinear problems, our method is based on the theory of linear holomorphic semigroups. This distinguishes it from the theory of nonlinear contraction semigroups whose basis is a nonlinear version of the Hille Yosida theorem: the Crandall-Liggett theorem. The latter theory is well-known and well-documented in the literature. Even though it is a powerful technique having found many applications, it is limited in its scope by the fact that, in concrete applications, it is closely tied to the maximum principle. Thus the theory of nonlinear contraction semigroups does not apply to systems, in general, since they do not allow for a maximum principle. For these reasons we do not include that theory.

Qualitative analysis for some quasilinear parabolic systems

1979
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Release : 1979
Genre :
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Book Synopsis Qualitative analysis for some quasilinear parabolic systems by : Piero de Mottoni

Download or read book Qualitative analysis for some quasilinear parabolic systems written by Piero de Mottoni. This book was released on 1979. Available in PDF, EPUB and Kindle. Book excerpt:

Maximal Function Methods for Sobolev Spaces

2021-08-02 Education
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Release : 2021-08-02
Genre : Education
Kind : eBook
Book Rating : 752/5 ( reviews)

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Book Synopsis Maximal Function Methods for Sobolev Spaces by : Juha Kinnunen

Download or read book Maximal Function Methods for Sobolev Spaces written by Juha Kinnunen. This book was released on 2021-08-02. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses advances in maximal function methods related to Poincaré and Sobolev inequalities, pointwise estimates and approximation for Sobolev functions, Hardy's inequalities, and partial differential equations. Capacities are needed for fine properties of Sobolev functions and characterization of Sobolev spaces with zero boundary values. The authors consider several uniform quantitative conditions that are self-improving, such as Hardy's inequalities, capacity density conditions, and reverse Hölder inequalities. They also study Muckenhoupt weight properties of distance functions and combine these with weighted norm inequalities; notions of dimension are then used to characterize density conditions and to give sufficient and necessary conditions for Hardy's inequalities. At the end of the book, the theory of weak solutions to the p p-Laplace equation and the use of maximal function techniques is this context are discussed. The book is directed to researchers and graduate students interested in applications of geometric and harmonic analysis in Sobolev spaces and partial differential equations.

Functional Analysis, Sobolev Spaces and Partial Differential Equations

2010-11-10 Mathematics
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Release : 2010-11-10
Genre : Mathematics
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Book Rating : 134/5 ( reviews)

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Book Synopsis Functional Analysis, Sobolev Spaces and Partial Differential Equations by : Haim Brezis

Download or read book Functional Analysis, Sobolev Spaces and Partial Differential Equations written by Haim Brezis. This book was released on 2010-11-10. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is a completely revised, updated, and expanded English edition of the important Analyse fonctionnelle (1983). In addition, it contains a wealth of problems and exercises (with solutions) to guide the reader. Uniquely, this book presents in a coherent, concise and unified way the main results from functional analysis together with the main results from the theory of partial differential equations (PDEs). Although there are many books on functional analysis and many on PDEs, this is the first to cover both of these closely connected topics. Since the French book was first published, it has been translated into Spanish, Italian, Japanese, Korean, Romanian, Greek and Chinese. The English edition makes a welcome addition to this list.

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