Geometric Partial Differential Equations Part 2

Author : Andrea Bonito,Ricardo Horacio Nochetto
Publisher : Elsevier
Page : 572 pages
File Size : 47,7 Mb
Release : 2021-01-26
Category : Mathematics
ISBN : 9780444643063

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Geometric Partial Differential Equations - Part 2 by Andrea Bonito,Ricardo Horacio Nochetto Pdf

Besides their intrinsic mathematical interest, geometric partial differential equations (PDEs) are ubiquitous in many scientific, engineering and industrial applications. They represent an intellectual challenge and have received a great deal of attention recently. The purpose of this volume is to provide a missing reference consisting of self-contained and comprehensive presentations. It includes basic ideas, analysis and applications of state-of-the-art fundamental algorithms for the approximation of geometric PDEs together with their impacts in a variety of fields within mathematics, science, and engineering. About every aspect of computational geometric PDEs is discussed in this and a companion volume. Topics in this volume include stationary and time-dependent surface PDEs for geometric flows, large deformations of nonlinearly geometric plates and rods, level set and phase field methods and applications, free boundary problems, discrete Riemannian calculus and morphing, fully nonlinear PDEs including Monge-Ampere equations, and PDE constrained optimization Each chapter is a complete essay at the research level but accessible to junior researchers and students. The intent is to provide a comprehensive description of algorithms and their analysis for a specific geometric PDE class, starting from basic concepts and concluding with interesting applications. Each chapter is thus useful as an introduction to a research area as well as a teaching resource, and provides numerous pointers to the literature for further reading The authors of each chapter are world leaders in their field of expertise and skillful writers. This book is thus meant to provide an invaluable, readable and enjoyable account of computational geometric PDEs

Author : Anonim
Publisher : Elsevier
Page : 710 pages
File Size : 52,8 Mb
Release : 2020-01-14
Category : Mathematics
ISBN : 9780444640048

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Geometric Partial Differential Equations - Part I by Anonim Pdf

Besides their intrinsic mathematical interest, geometric partial differential equations (PDEs) are ubiquitous in many scientific, engineering and industrial applications. They represent an intellectual challenge and have received a great deal of attention recently. The purpose of this volume is to provide a missing reference consisting of self-contained and comprehensive presentations. It includes basic ideas, analysis and applications of state-of-the-art fundamental algorithms for the approximation of geometric PDEs together with their impacts in a variety of fields within mathematics, science, and engineering. About every aspect of computational geometric PDEs is discussed in this and a companion volume. Topics in this volume include stationary and time-dependent surface PDEs for geometric flows, large deformations of nonlinearly geometric plates and rods, level set and phase field methods and applications, free boundary problems, discrete Riemannian calculus and morphing, fully nonlinear PDEs including Monge-Ampere equations, and PDE constrained optimization Each chapter is a complete essay at the research level but accessible to junior researchers and students. The intent is to provide a comprehensive description of algorithms and their analysis for a specific geometric PDE class, starting from basic concepts and concluding with interesting applications. Each chapter is thus useful as an introduction to a research area as well as a teaching resource, and provides numerous pointers to the literature for further reading The authors of each chapter are world leaders in their field of expertise and skillful writers. This book is thus meant to provide an invaluable, readable and enjoyable account of computational geometric PDEs

Author : Walter A. Strauss
Publisher : John Wiley & Sons
Page : 467 pages
File Size : 43,6 Mb
Release : 2007-12-21
Category : Mathematics
ISBN : 9780470054567

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Partial Differential Equations by Walter A. Strauss Pdf

Our understanding of the fundamental processes of the natural world is based to a large extent on partial differential equations (PDEs). The second edition of Partial Differential Equations provides an introduction to the basic properties of PDEs and the ideas and techniques that have proven useful in analyzing them. It provides the student a broad perspective on the subject, illustrates the incredibly rich variety of phenomena encompassed by it, and imparts a working knowledge of the most important techniques of analysis of the solutions of the equations. In this book mathematical jargon is minimized. Our focus is on the three most classical PDEs: the wave, heat and Laplace equations. Advanced concepts are introduced frequently but with the least possible technicalities. The book is flexibly designed for juniors, seniors or beginning graduate students in science, engineering or mathematics.

Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 41,6 Mb
Release : 1977
Category : Electronic
ISBN : OCLC:164041328

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Partial differential Equations and geometry by Anonim Pdf

Author : Christopher I. Byrnes
Publisher : Marcel Dekker
Page : 348 pages
File Size : 54,9 Mb
Release : 1979
Category : Mathematics
ISBN : UOM:39015049311767

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Partial Differential Equations and Geometry by Christopher I. Byrnes Pdf

Author : Robert Hardt,Michael Wolf
Publisher : American Mathematical Soc.
Page : 356 pages
File Size : 41,8 Mb
Release : 1994
Category : Mathematics
ISBN : 0821886843

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Nonlinear Partial Differential Equations in Differential Geometry by Robert Hardt,Michael Wolf Pdf

This book contains lecture notes of minicourses at the Regional Geometry Institute at Park City, Utah, in July 1992. Presented here are surveys of breaking developments in a number of areas of nonlinear partial differential equations in differential geometry. The authors of the articles are not only excellent expositors, but are also leaders in this field of research. All of the articles provide in-depth treatment of the topics and require few prerequisites and less background than current research articles.

Author : Misha Gromov
Publisher : Springer Science & Business Media
Page : 372 pages
File Size : 46,7 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9783662022672

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Partial Differential Relations by Misha Gromov Pdf

The classical theory of partial differential equations is rooted in physics, where equations (are assumed to) describe the laws of nature. Law abiding functions, which satisfy such an equation, are very rare in the space of all admissible functions (regardless of a particular topology in a function space). Moreover, some additional (like initial or boundary) conditions often insure the uniqueness of solutions. The existence of these is usually established with some apriori estimates which locate a possible solution in a given function space. We deal in this book with a completely different class of partial differential equations (and more general relations) which arise in differential geometry rather than in physics. Our equations are, for the most part, undetermined (or, at least, behave like those) and their solutions are rather dense in spaces of functions. We solve and classify solutions of these equations by means of direct (and not so direct) geometric constructions. Our exposition is elementary and the proofs of the basic results are selfcontained. However, there is a number of examples and exercises (of variable difficulty), where the treatment of a particular equation requires a certain knowledge of pertinent facts in the surrounding field. The techniques we employ, though quite general, do not cover all geometrically interesting equations. The border of the unexplored territory is marked by a number of open questions throughout the book.

Author : Alessio Figalli,Enrico Valdinoci,Ireneo Peral
Publisher : Springer
Page : 216 pages
File Size : 53,9 Mb
Release : 2018-05-23
Category : Mathematics
ISBN : 9783319740423

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Partial Differential Equations and Geometric Measure Theory by Alessio Figalli,Enrico Valdinoci,Ireneo Peral Pdf

This book collects together lectures by some of the leaders in the field of partial differential equations and geometric measure theory. It features a wide variety of research topics in which a crucial role is played by the interaction of fine analytic techniques and deep geometric observations, combining the intuitive and geometric aspects of mathematics with analytical ideas and variational methods. The problems addressed are challenging and complex, and often require the use of several refined techniques to overcome the major difficulties encountered. The lectures, given during the course "Partial Differential Equations and Geometric Measure Theory'' in Cetraro, June 2–7, 2014, should help to encourage further research in the area. The enthusiasm of the speakers and the participants of this CIME course is reflected in the text.

Author : Stefan Hildebrandt
Publisher : Springer Science & Business Media
Page : 696 pages
File Size : 48,6 Mb
Release : 2003
Category : Mathematics
ISBN : 3540440518

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Geometric Analysis and Nonlinear Partial Differential Equations by Stefan Hildebrandt Pdf

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.

Author : Friedrich Sauvigny
Publisher : Springer Science & Business Media
Page : 392 pages
File Size : 41,8 Mb
Release : 2006-10-11
Category : Mathematics
ISBN : 9783540344629

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Partial Differential Equations 2 by Friedrich Sauvigny Pdf

This encyclopedic work covers the whole area of Partial Differential Equations - of the elliptic, parabolic, and hyperbolic type - in two and several variables. Emphasis is placed on the connection of PDEs and complex variable methods. This second volume addresses Solvability of operator equations in Banach spaces; Linear operators in Hilbert spaces and spectral theory; Schauder's theory of linear elliptic differential equations; Weak solutions of differential equations; Nonlinear partial differential equations and characteristics; Nonlinear elliptic systems with differential-geometric applications. While partial differential equations are solved via integral representations in the preceding volume, this volume uses functional analytic solution methods.

Author : Guillermo Sapiro
Publisher : Unknown
Page : 385 pages
File Size : 45,6 Mb
Release : 2001-01-01
Category : Law
ISBN : 0521790751

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Geometric Partial Differential Equations and Image Analysis by Guillermo Sapiro Pdf

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.

Author : Joaqu’n PŽrez,JosŽ A. Galvez
Publisher : American Mathematical Soc.
Page : 185 pages
File Size : 53,9 Mb
Release : 2012-07-16
Category : Mathematics
ISBN : 9780821849927

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Geometric Analysis by Joaqu’n PŽrez,JosŽ A. Galvez Pdf

This volume contains research and expository articles from the courses and talks given at the RSME Lluis A. Santalo Summer School, ``Geometric Analysis'', held June 28-July 2, 2010, in Granada, Spain. The goal of the Summer School was to present some of the many advances currently taking place in the interaction between partial differential equations and differential geometry, with special emphasis on the theory of minimal surfaces. This volume includes expository articles about the current state of specific problems involving curvature and partial differential equations, with interactions to neighboring fields such as probability. An introductory, mostly self-contained course on constant mean curvature surfaces in Lie groups equipped with a left invariant metric is provided. The volume will be of interest to researchers, post-docs, and advanced PhD students in the interface between partial differential equations and differential geometry.

Author : Robert Everist Greene,Shing-Tung Yau
Publisher : American Mathematical Soc.
Page : 560 pages
File Size : 44,5 Mb
Release : 1993
Category : Mathematics
ISBN : 9780821814949

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Differential Geometry: Partial Differential Equations on Manifolds by Robert Everist Greene,Shing-Tung Yau Pdf

The first of three parts comprising Volume 54, the proceedings of the Summer Research Institute on Differential Geometry, held at the University of California, Los Angeles, July 1990 (ISBN for the set is 0-8218-1493-1). Part 1 begins with a problem list by S.T. Yau, successor to his 1980 list ( Sem

Author : Ovidiu Calin,Der-Chen Chang
Publisher : Springer Science & Business Media
Page : 52 pages
File Size : 52,8 Mb
Release : 2005
Category : Mathematics
ISBN : 0817643540

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Geometric Mechanics on Riemannian Manifolds by Ovidiu Calin,Der-Chen Chang Pdf

* A geometric approach to problems in physics, many of which cannot be solved by any other methods * Text is enriched with good examples and exercises at the end of every chapter * Fine for a course or seminar directed at grad and adv. undergrad students interested in elliptic and hyperbolic differential equations, differential geometry, calculus of variations, quantum mechanics, and physics

Author : P.A. Clarkson
Publisher : Springer Science & Business Media
Page : 466 pages
File Size : 49,6 Mb
Release : 2012-12-06
Category : Science
ISBN : 9789401120821

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Applications of Analytic and Geometric Methods to Nonlinear Differential Equations by P.A. Clarkson Pdf

In the study of integrable systems, two different approaches in particular have attracted considerable attention during the past twenty years. (1) The inverse scattering transform (IST), using complex function theory, which has been employed to solve many physically significant equations, the `soliton' equations. (2) Twistor theory, using differential geometry, which has been used to solve the self-dual Yang--Mills (SDYM) equations, a four-dimensional system having important applications in mathematical physics. Both soliton and the SDYM equations have rich algebraic structures which have been extensively studied. Recently, it has been conjectured that, in some sense, all soliton equations arise as special cases of the SDYM equations; subsequently many have been discovered as either exact or asymptotic reductions of the SDYM equations. Consequently what seems to be emerging is that a natural, physically significant system such as the SDYM equations provides the basis for a unifying framework underlying this class of integrable systems, i.e. `soliton' systems. This book contains several articles on the reduction of the SDYM equations to soliton equations and the relationship between the IST and twistor methods. The majority of nonlinear evolution equations are nonintegrable, and so asymptotic, numerical perturbation and reduction techniques are often used to study such equations. This book also contains articles on perturbed soliton equations. Painlevé analysis of partial differential equations, studies of the Painlevé equations and symmetry reductions of nonlinear partial differential equations. (ABSTRACT) In the study of integrable systems, two different approaches in particular have attracted considerable attention during the past twenty years; the inverse scattering transform (IST), for `soliton' equations and twistor theory, for the self-dual Yang--Mills (SDYM) equations. This book contains several articles on the reduction of the SDYM equations to soliton equations and the relationship between the IST and twistor methods. Additionally, it contains articles on perturbed soliton equations, Painlevé analysis of partial differential equations, studies of the Painlevé equations and symmetry reductions of nonlinear partial differential equations.