Author: Herbert AmannPublisher:
ISBN: 9788073780890
Category :
Languages : en
Pages : 139
Book Description
Anisotropic Function Spaces and Maximal Regularity for Parabolic Problems
Author: Herbert AmannPublisher:
ISBN: 9788073780890
Category :
Languages : en
Pages : 139
Book Description
Analytic Semigroups and Optimal Regularity in Parabolic Problems
Author: Alessandra LunardiPublisher: Springer Science & Business Media
ISBN: 9783764351724
Category : Mathematics
Languages : en
Pages : 452
Book Description
The book shows how the abstract methods of analytic semigroups and evolution equations in Banach spaces can be fruitfully applied to the study of parabolic problems. Particular attention is paid to optimal regularity results in linear equations. Furthermore, these results are used to study several other problems, especially fully nonlinear ones. Owing to the new unified approach chosen, known theorems are presented from a novel perspective and new results are derived. The book is self-contained. It is addressed to PhD students and researchers interested in abstract evolution equations and in parabolic partial differential equations and systems. It gives a comprehensive overview on the present state of the art in the field, teaching at the same time how to exploit its basic techniques. - - - This very interesting book provides a systematic treatment of the basic theory of analytic semigroups and abstract parabolic equations in general Banach spaces, and how this theory may be used in the study of parabolic partial differential equations; it takes into account the developments of the theory during the last fifteen years. (...) For instance, optimal regularity results are a typical feature of abstract parabolic equations; they are comprehensively studied in this book, and yield new and old regularity results for parabolic partial differential equations and systems. (Mathematical Reviews) Motivated by applications to fully nonlinear problems the approach is focused on classical solutions with continuous or Hölder continuous derivatives. (Zentralblatt MATH)
Parabolic Problems
Author: Joachim EscherPublisher: Springer Science & Business Media
ISBN: 3034800754
Category : Mathematics
Languages : en
Pages : 712
Book Description
The volume originates from the 'Conference on Nonlinear Parabolic Problems' held in celebration of Herbert Amann's 70th birthday at the Banach Center in Bedlewo, Poland. It features a collection of peer-reviewed research papers by recognized experts highlighting recent advances in fields of Herbert Amann's interest such as nonlinear evolution equations, fluid dynamics, quasi-linear parabolic equations and systems, functional analysis, and more.
Linear Discrete Parabolic Problems
Author: Nikolai BakaevPublisher: Elsevier
ISBN: 0080462081
Category : Mathematics
Languages : en
Pages : 303
Book Description
This volume introduces a unified, self-contained study of linear discrete parabolic problems through reducing the starting discrete problem to the Cauchy problem for an evolution equation in discrete time. Accessible to beginning graduate students, the book contains a general stability theory of discrete evolution equations in Banach space and gives applications of this theory to the analysis of various classes of modern discretization methods, among others, Runge-Kutta and linear multistep methods as well as operator splitting methods. Key features: * Presents a unified approach to examining discretization methods for parabolic equations. * Highlights a stability theory of discrete evolution equations (discrete semigroups) in Banach space. * Deals with both autonomous and non-autonomous equations as well as with equations with memory. * Offers a series of numerous well-posedness and convergence results for various discretization methods as applied to abstract parabolic equations; among others, Runge-Kutta and linear multistep methods as well as certain operator splitting methods. * Provides comments of results and historical remarks after each chapter. · Presents a unified approach to examining discretization methods for parabolic equations. · Highlights a stability theory of discrete evolution equations (discrete semigroups) in Banach space. · Deals with both autonomous and non-autonomous equations as well as with equations with memory. · Offers a series of numerous well-posedness and convergence results for various discretization methods as applied to abstract parabolic equations; among others, Runge-Kutta and linear multistep methods as well as certain operator splitting methods as well as certain operator splitting methods are studied in detail. ·Provides comments of results and historical remarks after each chapter.
Maximal Regularity for Nonsmooth Parabolic Problems in Sobolev-Morrey Spaces
Author: Linear and Quasilinear Parabolic Problems
Author: Herbert AmannPublisher: Springer Science & Business Media
ISBN: 9783764351144
Category : Language Arts & Disciplines
Languages : en
Pages : 688
Book Description
This treatise gives an exposition of the functional analytical approach to quasilinear parabolic evolution equations, developed to a large extent by the author during the last 10 years. This approach is based on the theory of linear nonautonomous parabolic evolution equations and on interpolation-extrapolation techniques. It is the only general method that applies to noncoercive quasilinear parabolic systems under nonlinear boundary conditions. The present first volume is devoted to a detailed study of nonautonomous linear parabolic evolution equations in general Banach spaces. It contains a careful exposition of the constant domain case, leading to some improvements of the classical Sobolevskii-Tanabe results. It also includes recent results for equations possessing constant interpolation spaces. In addition, systematic presentations of the theory of maximal regularity in spaces of continuous and Hölder continuous functions, and in Lebesgue spaces, are given. It includes related recent theorems in the field of harmonic analysis in Banach spaces and on operators possessing bounded imaginary powers. Lastly, there is a complete presentation of the technique of interpolation-extrapolation spaces and of evolution equations in those spaces, containing many new results.
Linear and Quasilinear Parabolic Problems
Author: Herbert AmannPublisher: Springer
ISBN: 3030117634
Category : Mathematics
Languages : en
Pages : 462
Book Description
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.
Analytic Semigroup Approach to Higher Order Parabolic Problems
Author: Tomoro AsaiPublisher: LAP Lambert Academic Publishing
ISBN: 9783659511639
Category :
Languages : en
Pages : 100
Book Description
The subject of this book is to apply the analytic semigroup theory to solve various kinds of fourth order problems. In Chapter 2, we study the Cauchy problem for the surface diffusion flow and the Willmore flow in one dimensional case. In particular, we focus our attention to relax the regularity assumption on the initial curve. In Chapter 3, we extend the results of Chapter 2 for multi-dimensional case of various kinds of fourth order parabolic equations via maximal regularity. In the last Chapter, we consider the self-similar solution for the surface diffusion flow with boundary conditions.
Author: Philippe Clément
Author: Robert Denk