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Second Order Partial Differential Equations In Hilbert Spaces
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Book Synopsis Second Order Partial Differential Equations in Hilbert Spaces by : Giuseppe Da Prato
Download or read book Second Order Partial Differential Equations in Hilbert Spaces written by Giuseppe Da Prato and published by Cambridge University Press. This book was released on 2002-07-25 with total page 397 pages. Available in PDF, EPUB and Kindle. Book excerpt: State of the art treatment of a subject which has applications in mathematical physics, biology and finance. Includes discussion of applications to control theory. There are numerous notes and references that point to further reading. Coverage of some essential background material helps to make the book self contained.
Book Synopsis Partial Differential Equations by : Rainer Picard
Download or read book Partial Differential Equations written by Rainer Picard and published by Walter de Gruyter. This book was released on 2011-06-30 with total page 489 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a systematic approach to a solution theory for linear partial differential equations developed in a Hilbert space setting based on a Sobolev lattice structure, a simple extension of the well-established notion of a chain (or scale) of Hilbert spaces. The focus on a Hilbert space setting (rather than on an apparently more general Banach space) is not a severe constraint, but rather a highly adaptable and suitable approach providing a more transparent framework for presenting the main issues in the development of a solution theory for partial differential equations. In contrast to other texts on partial differential equations, which consider either specific equation types or apply a collection of tools for solving a variety of equations, this book takes a more global point of view by focusing on the issues involved in determining the appropriate functional analytic setting in which a solution theory can be naturally developed. Applications to many areas of mathematical physics are also presented. The book aims to be largely self-contained. Full proofs to all but the most straightforward results are provided, keeping to a minimum references to other literature for essential material. It is therefore highly suitable as a resource for graduate courses and also for researchers, who will find new results for particular evolutionary systems from mathematical physics.
Book Synopsis Second Order PDE's in Finite and Infinite Dimension by : Sandra Cerrai
Download or read book Second Order PDE's in Finite and Infinite Dimension written by Sandra Cerrai and published by Springer. This book was released on 2003-07-01 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main objective of this monograph is the study of a class of stochastic differential systems having unbounded coefficients, both in finite and in infinite dimension. We focus our attention on the regularity properties of the solutions and hence on the smoothing effect of the corresponding transition semigroups in the space of bounded and uniformly continuous functions. As an application of these results, we study the associated Kolmogorov equations, the large-time behaviour of the solutions and some stochastic optimal control problems together with the corresponding Hamilton- Jacobi-Bellman equations. In the literature there exists a large number of works (mostly in finite dimen sion) dealing with these arguments in the case of bounded Lipschitz-continuous coefficients and some of them concern the case of coefficients having linear growth. Few papers concern the case of non-Lipschitz coefficients, but they are mainly re lated to the study of the existence and the uniqueness of solutions for the stochastic system. Actually, the study of any further properties of those systems, such as their regularizing properties or their ergodicity, seems not to be developed widely enough. With these notes we try to cover this gap.
Book Synopsis Elliptic Partial Differential Equations of Second Order by : David Gilbarg
Download or read book Elliptic Partial Differential Equations of Second Order written by David Gilbarg and published by Springer. This book was released on 2015-03-30 with total page 531 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the reviews: "This is a book of interest to any having to work with differential equations, either as a reference or as a book to learn from. The authors have taken trouble to make the treatment self-contained. It (is) suitable required reading for a PhD student." --New Zealand Mathematical Society, 1985
Book Synopsis Complete Second Order Linear Differential Equations in Hilbert Spaces by : Alexander Ya. Shklyar
Download or read book Complete Second Order Linear Differential Equations in Hilbert Spaces written by Alexander Ya. Shklyar and published by Birkhäuser. This book was released on 2012-12-06 with total page 225 pages. Available in PDF, EPUB and Kindle. Book excerpt: Incomplete second order linear differential equations in Banach spaces as well as first order equations have become a classical part of functional analysis. This monograph is an attempt to present a unified systematic theory of second order equations y" (t) + Ay' (t) + By (t) = 0 including well-posedness of the Cauchy problem as well as the Dirichlet and Neumann problems. Exhaustive yet clear answers to all posed questions are given. Special emphasis is placed on new surprising effects arising for complete second order equations which do not take place for first order and incomplete second order equations. For this purpose, some new results in the spectral theory of pairs of operators and the boundary behavior of integral transforms have been developed. The book serves as a self-contained introductory course and a reference book on this subject for undergraduate and post- graduate students and research mathematicians in analysis. Moreover, users will welcome having a comprehensive study of the equations at hand, and it gives insight into the theory of complete second order linear differential equations in a general context - a theory which is far from being fully understood.
Book Synopsis Hilbert Space Methods in Partial Differential Equations by : Ralph E. Showalter
Download or read book Hilbert Space Methods in Partial Differential Equations written by Ralph E. Showalter and published by Courier Corporation. This book was released on 2010-03-18 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: This graduate-level text opens with an elementary presentation of Hilbert space theory sufficient for understanding the rest of the book. Additional topics include boundary value problems, evolution equations, optimization, and approximation.1979 edition.
Book Synopsis Second Order Partial Differential Equations in Hilbert Spaces by : Giuseppe Da Prato
Download or read book Second Order Partial Differential Equations in Hilbert Spaces written by Giuseppe Da Prato and published by Cambridge University Press. This book was released on 2002-07-25 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: Second order linear parabolic and elliptic equations arise frequently in mathematics and other disciplines. For example parabolic equations are to be found in statistical mechanics and solid state theory, their infinite dimensional counterparts are important in fluid mechanics, mathematical finance and population biology, whereas nonlinear parabolic equations arise in control theory. Here the authors present a state of the art treatment of the subject from a new perspective. The main tools used are probability measures in Hilbert and Banach spaces and stochastic evolution equations. There is then a discussion of how the results in the book can be applied to control theory. This area is developing very rapidly and there are numerous notes and references that point the reader to more specialised results not covered in the book. Coverage of some essential background material will help make the book self-contained and increase its appeal to those entering the subject.
Book Synopsis Introduction to Partial Differential Equations and Hilbert Space Methods by : Karl E. Gustafson
Download or read book Introduction to Partial Differential Equations and Hilbert Space Methods written by Karl E. Gustafson and published by Courier Corporation. This book was released on 2012-04-26 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: Easy-to-use text examines principal method of solving partial differential equations, 1st-order systems, computation methods, and much more. Over 600 exercises, with answers for many. Ideal for a 1-semester or full-year course.
Book Synopsis Nonlinear Evolution and Difference Equations of Monotone Type in Hilbert Spaces by : Behzad Djafari-Rouhani
Download or read book Nonlinear Evolution and Difference Equations of Monotone Type in Hilbert Spaces written by Behzad Djafari-Rouhani and published by CRC Press. This book was released on 2021-03-31 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with first and second order evolution and difference monotone type equations. The approach followed in the book was first introduced by Dr. Djafari-Rouhani, and later advanced by him along with Dr. Khatibzadeh.
Book Synopsis Introduction To Second Order Partial Differential Equations, An: Classical And Variational Solutions by : Doina Cioranescu
Download or read book Introduction To Second Order Partial Differential Equations, An: Classical And Variational Solutions written by Doina Cioranescu and published by World Scientific Publishing Company. This book was released on 2017-11-27 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book extensively introduces classical and variational partial differential equations (PDEs) to graduate and post-graduate students in Mathematics. The topics, even the most delicate, are presented in a detailed way. The book consists of two parts which focus on second order linear PDEs. Part I gives an overview of classical PDEs, that is, equations which admit strong solutions, verifying the equations pointwise. Classical solutions of the Laplace, heat, and wave equations are provided. Part II deals with variational PDEs, where weak (variational) solutions are considered. They are defined by variational formulations of the equations, based on Sobolev spaces. A comprehensive and detailed presentation of these spaces is given. Examples of variational elliptic, parabolic, and hyperbolic problems with different boundary conditions are discussed.
Book Synopsis Second Order Partial Differential Equations in Hilbert Spaces. London Mathematical Society Lecture Note Series by : Giuseppe Da Prato
Download or read book Second Order Partial Differential Equations in Hilbert Spaces. London Mathematical Society Lecture Note Series written by Giuseppe Da Prato and published by . This book was released on 2002 with total page 397 pages. Available in PDF, EPUB and Kindle. Book excerpt: Second order linear parabolic and elliptic equations arise frequently in mathematics and other disciplines. For example parabolic equations are to be found in statistical mechanics and solid state theory, their infinite dimensional counterparts are important in fluid mechanics, mathematical finance and population biology, whereas nonlinear parabolic equations arise in control theory. Here the authors present a state of the art treatment of the subject from a new perspective. The main tools used are probability measures in Hilbert and Banach spaces and stochastic evolution equations. There is t.
Book Synopsis Partial Differential Equations by : Lipman Bers
Download or read book Partial Differential Equations written by Lipman Bers and published by American Mathematical Soc.. This book was released on 1964-12-31 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book consists of two main parts. The first part, "Hyperbolic and Parabolic Equations", written by F. John, contains a well-chosen assortment of material intended to give an understanding of some problems and techniques involving hyperbolic and parabolic equations. The emphasis is on illustrating the subject without attempting to survey it. The point of view is classical, and this serves well in furnishing insight into the subject; it also makes it possible for the lectures to be read by someone familiar with only the fundamentals of real and complex analysis. The second part, "Elliptic Equations", written by L. Bers and M. Schechter, contains a very readable account of the results and methods of the theory of linear elliptic equations, including the maximum principle, Hilbert-space methods, and potential-theoretic methods. It also contains a brief discussion of some quasi-linear elliptic equations. The book is suitable for graduate students and researchers interested in partial differential equations.
Book Synopsis Second Order Partial Differential Equations in Hilbert Spaces by : Giuseppe Da Prato
Download or read book Second Order Partial Differential Equations in Hilbert Spaces written by Giuseppe Da Prato and published by . This book was released on 2002 with total page 379 pages. Available in PDF, EPUB and Kindle. Book excerpt: State of the art treatment of a subject which has applications in mathematical physics, biology and finance. Includes discussion of applications to control theory. There are numerous notes and references that point to further reading. Coverage of some essential background material helps to make the book self contained.
Book Synopsis Partial Differential Equations by : Joseph Wloka
Download or read book Partial Differential Equations written by Joseph Wloka and published by Cambridge University Press. This book was released on 1987-05-21 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt: A rigorous introduction to the abstract theory of partial differential equations progresses from the theory of distribution and Sobolev spaces to Fredholm operations, the Schauder fixed point theorem and Bochner integrals.
Book Synopsis An Introduction to Partial Differential Equations by : Yehuda Pinchover
Download or read book An Introduction to Partial Differential Equations written by Yehuda Pinchover and published by Cambridge University Press. This book was released on 2005-05-12 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: A complete introduction to partial differential equations, this textbook provides a rigorous yet accessible guide to students in mathematics, physics and engineering. The presentation is lively and up to date, paying particular emphasis to developing an appreciation of underlying mathematical theory. Beginning with basic definitions, properties and derivations of some basic equations of mathematical physics from basic principles, the book studies first order equations, classification of second order equations, and the one-dimensional wave equation. Two chapters are devoted to the separation of variables, whilst others concentrate on a wide range of topics including elliptic theory, Green's functions, variational and numerical methods. A rich collection of worked examples and exercises accompany the text, along with a large number of illustrations and graphs to provide insight into the numerical examples. Solutions to selected exercises are included for students whilst extended solution sets are available to lecturers from [email protected].
Book Synopsis Partial Differential Equations by : Bhamra
Download or read book Partial Differential Equations written by Bhamra and published by PHI Learning Pvt. Ltd.. This book was released on 2010-01-30 with total page 580 pages. Available in PDF, EPUB and Kindle. Book excerpt: and postgraduate (MA/MSc) students of mathematics, and conforms to the course curriculum prescribed by UGC. The text is broadly organized into two parts. The first part (Lessons 1 to 15) mostly covers the first-order equations in two variables. In these lessons, the mathematical importance of PDEs of first order in physics and applied sciences has also been highlighted. The other part (Lessons 16 to 50) deals with the various properties of second-order and first- order PDEs. The book emphasizes the applications of PDEs and covers various important topics such as the Hamilton Jacobi equation, Conservation laws, Similarity solution, Asymptotics and Power series solution and many more. The graded problems, the techniques for solving them, and a large number of exercises with hints and answers help students gain the necessary skill and confidence in handling the subject.
Book Synopsis Introduction to Partial Differential Equations by : G. B. Folland
Download or read book Introduction to Partial Differential Equations written by G. B. Folland and published by Princeton University Press. This book was released on 1995-11-04 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this text is to aquaint the student with the fundamental classical results of partial differential equations and to guide them into some of the modern theory, enabling them to read more advanced works on the subject.--Provided by publisher.
