Phase space analysis of partial differential equations, Colombini Ferruccio, Pernazza Ludovico
Автор: Strang Название: Differential Equations and Linear Algebra ISBN: 0980232791 ISBN-13(EAN): 9780980232790 Издательство: Cambridge Academ Рейтинг: Цена: 5203 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Differential equations and linear algebra are two central topics in the undergraduate mathematics curriculum. This innovative textbook allows the two subjects to be developed either separately or together, illuminating the connections between two fundamental topics, and giving increased flexibility to instructors. It can be used either as a semester-long course in differential equations, or as a one-year course in differential equations, linear algebra, and applications. Beginning with the basics of differential equations, it covers first and second order equations, graphical and numerical methods, and matrix equations. The book goes on to present the fundamentals of vector spaces, followed by eigenvalues and eigenvectors, positive definiteness, integral transform methods and applications to PDEs. The exposition illuminates the natural correspondence between solution methods for systems of equations in discrete and continuous settings. The topics draw on the physical sciences, engineering and economics, reflecting the author's distinguished career as an applied mathematician and expositor.
Описание: Numerical analysis presents different faces to the world. For mathematicians it is a bona fide mathematical theory with an applicable flavour. For scientists and engineers it is a practical, applied subject, part of the standard repertoire of modelling techniques. For computer scientists it is a theory on the interplay of computer architecture and algorithms for real-number calculations. The tension between these standpoints is the driving force of this book, which presents a rigorous account of the fundamentals of numerical analysis of both ordinary and partial differential equations. The exposition maintains a balance between theoretical, algorithmic and applied aspects. This new edition has been extensively updated, and includes new chapters on emerging subject areas: geometric numerical integration, spectral methods and conjugate gradients. Other topics covered include multistep and Runge-Kutta methods; finite difference and finite elements techniques for the Poisson equation; and a variety of algorithms to solve large, sparse algebraic systems.
Описание: This volume contains refereed research articles written by experts in the field of applied analysis, differential equations and related topics. Well-known leading
mathematicians worldwide and prominent young scientists cover a diverse range of topics, including the most exciting recent developments. A broad range of topics of recent interest
are treated: existence, uniqueness, viability, asymptotic stability, viscosity solutions, controllability and numerical analysis for ODE, PDE and stochastic equations.
of the book is wide, ranging from pure mathematics to various applied fields such as classical mechanics, biomedicine, and population dynamics.
Описание: This modern introduction to Fourier analysis and partial differential equations is intended to be used with courses for beginning graduate students. With minimal prerequisites the authors take the reader from fundamentals to research topics in the area of nonlinear evolution equations. The first part of the book consists of some very classical material, followed by a discussion of the theory of periodic distributions and the periodic Sobolev spaces. The authors then turn to the study of linear and nonlinear equations in the setting provided by periodic distributions. They assume only some familiarity with Banach and Hilbert spaces and the elementary properties of bounded linear operators. After presenting a fairly complete discussion of local and global well-posedness for the nonlinear Schrodinger and the Korteweg-de Vries equations, they turn their attention, in the two final chapters, to the non-periodic setting, concentrating on problems that do not occur in the periodic case.
Описание: This collection of original articles and surveys treats linear and nonlinear aspects of the theory of partial differential equations. Phase space analysis methods,
also known as microlocal analysis, have yielded striking results over the past years and have become one of the main tools of investigation. Equally important is their role in many
applications to physics, for example, in quantum and spectral theory.
Описание: This book provides an introduction to the use of geometric partial differential equations in image processing and computer vision. This research area brings a number of new concepts into the field, providing a very fundamental and formal approach to image processing. State-of-the-art practical results in a large number of real problems are achieved with the techniques described in this book. Applications covered include image segmentation, shape analysis, image enhancement, and tracking. This book will be a useful resource for researchers and practitioners. It is intended to provide information for people investigating new solutions to image processing problems as well as for people searching for existent advanced solutions.
Описание: 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.
Описание: This well-organized and coherent collection of papers leads the reader to the frontiers of present research in the theory of nonlinear partial differential equations and the calculus of variations and offers insight into some exciting developments. In addition, most articles also provide an excellent introduction to their background, describing extensively as they do the history of those problems presented, as well as the state of the art and offer a well-chosen guide to the literature.Part I contains the contributions of geometric nature: From spectral theory on regular and singular spaces to regularity theory of solutions of variational problems. Part II consists of articles on partial differential equations which originate from problems in physics, biology and stochastics. They cover elliptic, hyperbolic and parabolic cases.
Описание: Capturing the state of the art of the interplay between partial differential equations, functional analysis, maximal regularity, and probability theory, this volume
was initiated at the Delft conference on the occasion of the retirement of Philippe Clement. It will be of interest to researchers in PDEs and functional analysis.
Описание: Contains some of the invited lectures presented at the International Conference Analysis, PDEs and Applications, held in Rome in July 2008, and dedicated to Vladimir G Maz`ya on the occasion of his 70th birthday. This title present surveys as well as fresh results in the areas in which Maz`ya gave seminal contributions.
Описание: S. Albertoni: Alcuni metodi di calcolo nella teoria della diffusione dei neutroni.- I. Babuska: Optimization and numerical stability in computations.- J.H. Bramble: Error estimates in elliptic boundary value problems.- G. Capriz: The numerical approach to hydrodynamic problems.- A. Dou: Energy inequalities in an elastic cylinder.- T. Doupont: On the existence of an iterative method for the solution of elliptic difference equation with an improved work estimate.- J. Douglas, J.R. Cannon: The approximation of harmonic and parabolic functions of half-spaces from interior data.- B.E. Hubbard: Error estimates in the fixed Membrane problem.- K. Jorgens: Calculation of the spectrum of a Schr?dinger operator.- A. Lasota: Contingent equations and boundary value problems.- J.L. Lions: R?duction ? des probl?mes du type Cauchy-Kowalewska.- J.L. Lions: Probl?mes aux limites non homog?nes ? donn?es irr?guli?res; une m?thode d’approximation.- J.L. Lions: Remarques sur l’approximation r?gularis?e de probl?mes aux limites.- W.V. Petryshyn: On the approximation-solvability of nonlinear functional equations in normed linear spaces.- P.A. Raviart: Approximation des ?quations d’?volution par des m?thodes variationnelles.- M. Sibony, H. Brezis: M?thodes d’approximation et d’it?ration pour les operateurs monotones.- V. Thomee: Some topics in stability theory for partial difference operators.
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