Linear And Quasilinear Parabolic Systems Sobolev Space Theory

Author : David Hoff
Publisher : American Mathematical Soc.
Page : 226 pages
File Size : 46,8 Mb
Release : 2020-11-18
Category : Education
ISBN : 9781470461614

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

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.

Author : Alexander Koshelev
Publisher : Springer
Page : 277 pages
File Size : 55,8 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540447726

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Regularity Problem for Quasilinear Elliptic and Parabolic Systems by Alexander Koshelev Pdf

The smoothness of solutions for quasilinear systems is one of the most important problems in modern mathematical physics. This book deals with regular or strong solutions for general quasilinear second-order elliptic and parabolic systems. Applications in solid mechanics, hydrodynamics, elasticity and plasticity are described. The results presented are based on two main ideas: the universal iterative method, and explicit, sometimes sharp, coercivity estimates in weighted spaces. Readers are assumed to have a standard background in analysis and PDEs.

Author : Herbert Amann
Publisher : Birkhäuser
Page : 366 pages
File Size : 51,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034892216

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Linear and Quasilinear Parabolic Problems by Herbert Amann Pdf

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.

Author : Juha Kinnunen,Juha Lehrbäck,Antti Vähäkangas
Publisher : American Mathematical Soc.
Page : 354 pages
File Size : 45,6 Mb
Release : 2021-08-02
Category : Education
ISBN : 9781470465759

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Maximal Function Methods for Sobolev Spaces by Juha Kinnunen,Juha Lehrbäck,Antti Vähäkangas Pdf

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.

Author : Haim Brezis
Publisher : Springer Science & Business Media
Page : 603 pages
File Size : 50,9 Mb
Release : 2010-11-10
Category : Mathematics
ISBN : 9780387709130

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Functional Analysis, Sobolev Spaces and Partial Differential Equations by Haim Brezis Pdf

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.

Author : Lindsay N. Childs,Cornelius Greither,Kevin P. Keating,Alan Koch,Timothy Kohl,Paul J. Truman,Robert G. Underwood
Publisher : American Mathematical Soc.
Page : 311 pages
File Size : 53,9 Mb
Release : 2021-11-10
Category : Education
ISBN : 9781470465162

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Hopf Algebras and Galois Module Theory by Lindsay N. Childs,Cornelius Greither,Kevin P. Keating,Alan Koch,Timothy Kohl,Paul J. Truman,Robert G. Underwood Pdf

Hopf algebras have been shown to play a natural role in studying questions of integral module structure in extensions of local or global fields. This book surveys the state of the art in Hopf-Galois theory and Hopf-Galois module theory and can be viewed as a sequel to the first author's book, Taming Wild Extensions: Hopf Algebras and Local Galois Module Theory, which was published in 2000. The book is divided into two parts. Part I is more algebraic and focuses on Hopf-Galois structures on Galois field extensions, as well as the connection between this topic and the theory of skew braces. Part II is more number theoretical and studies the application of Hopf algebras to questions of integral module structure in extensions of local or global fields. Graduate students and researchers with a general background in graduate-level algebra, algebraic number theory, and some familiarity with Hopf algebras will appreciate the overview of the current state of this exciting area and the suggestions for numerous avenues for further research and investigation.

Author : Pramod N. Achar
Publisher : American Mathematical Soc.
Page : 562 pages
File Size : 55,9 Mb
Release : 2021-09-27
Category : Education
ISBN : 9781470455972

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Perverse Sheaves and Applications to Representation Theory by Pramod N. Achar Pdf

Since its inception around 1980, the theory of perverse sheaves has been a vital tool of fundamental importance in geometric representation theory. This book, which aims to make this theory accessible to students and researchers, is divided into two parts. The first six chapters give a comprehensive account of constructible and perverse sheaves on complex algebraic varieties, including such topics as Artin's vanishing theorem, smooth descent, and the nearby cycles functor. This part of the book also has a chapter on the equivariant derived category, and brief surveys of side topics including étale and ℓ-adic sheaves, D-modules, and algebraic stacks. The last four chapters of the book show how to put this machinery to work in the context of selected topics in geometric representation theory: Kazhdan-Lusztig theory; Springer theory; the geometric Satake equivalence; and canonical bases for quantum groups. Recent developments such as the p-canonical basis are also discussed. The book has more than 250 exercises, many of which focus on explicit calculations with concrete examples. It also features a 4-page “Quick Reference” that summarizes the most commonly used facts for computations, similar to a table of integrals in a calculus textbook.

Author : Phillipe Clement
Publisher : CRC Press
Page : 473 pages
File Size : 51,7 Mb
Release : 2020-12-22
Category : Mathematics
ISBN : 9781000111125

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semigroup theory and applications by Phillipe Clement Pdf

This book contains articles on maximal regulatory problems, interpolation spaces, multiplicative perturbations of generators, linear and nonlinear evolution equations, integrodifferential equations, dual semigroups, positive semigroups, applications to control theory, and boundary value problems.

Author : George R. Sell,Yuncheng You
Publisher : Springer Science & Business Media
Page : 680 pages
File Size : 42,7 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9781475750379

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Dynamics of Evolutionary Equations by George R. Sell,Yuncheng You Pdf

The theory and applications of infinite dimensional dynamical systems have attracted the attention of scientists for quite some time. This book serves as an entrée for scholars beginning their journey into the world of dynamical systems, especially infinite dimensional spaces. The main approach involves the theory of evolutionary equations.

Author : Nabil H. Mustafa
Publisher : American Mathematical Society
Page : 251 pages
File Size : 53,9 Mb
Release : 2022-01-14
Category : Mathematics
ISBN : 9781470461560

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Sampling in Combinatorial and Geometric Set Systems by Nabil H. Mustafa Pdf

Understanding the behavior of basic sampling techniques and intrinsic geometric attributes of data is an invaluable skill that is in high demand for both graduate students and researchers in mathematics, machine learning, and theoretical computer science. The last ten years have seen significant progress in this area, with many open problems having been resolved during this time. These include optimal lower bounds for epsilon-nets for many geometric set systems, the use of shallow-cell complexity to unify proofs, simpler and more efficient algorithms, and the use of epsilon-approximations for construction of coresets, to name a few. This book presents a thorough treatment of these probabilistic, combinatorial, and geometric methods, as well as their combinatorial and algorithmic applications. It also revisits classical results, but with new and more elegant proofs. While mathematical maturity will certainly help in appreciating the ideas presented here, only a basic familiarity with discrete mathematics, probability, and combinatorics is required to understand the material.

Author : Ragnar-Olaf Buchweitz
Publisher : American Mathematical Society
Page : 175 pages
File Size : 41,6 Mb
Release : 2021-12-16
Category : Mathematics
ISBN : 9781470453404

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Maximal Cohen–Macaulay Modules and Tate Cohomology by Ragnar-Olaf Buchweitz Pdf

This book is a lightly edited version of the unpublished manuscript Maximal Cohen–Macaulay modules and Tate cohomology over Gorenstein rings by Ragnar-Olaf Buchweitz. The central objects of study are maximal Cohen–Macaulay modules over (not necessarily commutative) Gorenstein rings. The main result is that the stable category of maximal Cohen–Macaulay modules over a Gorenstein ring is equivalent to the stable derived category and also to the homotopy category of acyclic complexes of projective modules. This assimilates and significantly extends earlier work of Eisenbud on hypersurface singularities. There is also an extensive discussion of duality phenomena in stable derived categories, extending Tate duality on cohomology of finite groups. Another noteworthy aspect is an extension of the classical BGG correspondence to super-algebras. There are numerous examples that illustrate these ideas. The text includes a survey of developments subsequent to, and connected with, Buchweitz's manuscript.

Author : J. Scott Carter,Seiichi Kamada
Publisher : American Mathematical Society
Page : 365 pages
File Size : 51,5 Mb
Release : 2021-12-15
Category : Mathematics
ISBN : 9781470466718

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Diagrammatic Algebra by J. Scott Carter,Seiichi Kamada Pdf

This book is an introduction to techniques and results in diagrammatic algebra. It starts with abstract tensors and their categorifications, presents diagrammatic methods for studying Frobenius and Hopf algebras, and discusses their relations with topological quantum field theory and knot theory. The text is replete with figures, diagrams, and suggestive typography that allows the reader a glimpse into many higher dimensional processes. The penultimate chapter summarizes the previous material by demonstrating how to braid 3- and 4- dimensional manifolds into 5- and 6-dimensional spaces. The book is accessible to post-qualifier graduate students, and will also be of interest to algebraists, topologists and algebraic topologists who would like to incorporate diagrammatic techniques into their research.

Author : Vugar E. Ismailov
Publisher : American Mathematical Society
Page : 186 pages
File Size : 54,6 Mb
Release : 2021-12-17
Category : Mathematics
ISBN : 9781470467654

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Ridge Functions and Applications in Neural Networks by Vugar E. Ismailov Pdf

Recent years have witnessed a growth of interest in the special functions called ridge functions. These functions appear in various fields and under various guises. They appear in partial differential equations (where they are called plane waves), in computerized tomography, and in statistics. Ridge functions are also the underpinnings of many central models in neural network theory. In this book various approximation theoretic properties of ridge functions are described. This book also describes properties of generalized ridge functions, and their relation to linear superpositions and Kolmogorov's famous superposition theorem. In the final part of the book, a single and two hidden layer neural networks are discussed. The results obtained in this part are based on properties of ordinary and generalized ridge functions. Novel aspects of the universal approximation property of feedforward neural networks are revealed. This book will be of interest to advanced graduate students and researchers working in functional analysis, approximation theory, and the theory of real functions, and will be of particular interest to those wishing to learn more about neural network theory and applications and other areas where ridge functions are used.

Author : Nikolaĭ Vladimirovich Krylov
Publisher : Unknown
Page : 377 pages
File Size : 50,5 Mb
Release : 1900
Category : Differential equations, Elliptic
ISBN : 1470421216

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Lectures on Elliptic and Parabolic Equations in Sobolev Spaces by Nikolaĭ Vladimirovich Krylov Pdf

Author : Hans-Jürgen Schmeisser,Prof. Dr. Hans Triebel
Publisher : Teubner-Texte zur Mathematik
Page : 316 pages
File Size : 47,7 Mb
Release : 1993-09
Category : Technology & Engineering
ISBN : UOM:39015032475686

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Function Spaces, Differential Operators and Nonlinear Analysis by Hans-Jürgen Schmeisser,Prof. Dr. Hans Triebel Pdf

The present Teubner-Text contains invited surveys and shorter communications con­ nected with the International Conference "Function Spaces, Differential Operators and Non­ linear Analysis", which took place in Friedrichroda (Thuringia, Germany) from September 20-26, 1992. The main subjects are weil reflected by the table of contents. 55 mathematicians attended the conference, many of them from eastern countries. We take the opportunity to thank DFG for financial support, which enabled us to invite mathematicians from the former socialist countries, and especially from the former Soviet Union, and which gave us the pos­ sibility to maintain and to strengthen our contacts to these centers of the theory of function spaces and its application to PDE's, \li'DE's and approximation theory. The organization of the conference as weil as the final preparation of this text was mostly done by our co-workers in Jena. We wish to thank all of them for the generaus support they gave us far beyond their duties (whatever this means in connection with the organization of a conference). The final preparation of this text was mainly done by Dr. M. Malarski. Fur­ thermore Dr. M. Geisler, Ms. D. Haroske and Dr. W. Sicke! converted some manuscript in readable papers on TEX-standard Ievel. We wish to thank them for doing this time-consuming work. Jena, May 13, 1993 H.-J. Schmeisser H. Triebe! Contents Survey Articles 9 I Herbert Amann Nonhomogeneaus Linear and Quasilinear Elliptic and Parabolic Boundary Value Pr- lems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Gerard Bourdaud The Functional Calculus in Sobolev Spaces . . . . . . . . . . . . . . . . . . . 127 . . . . .