Download or read book Sobolev Gradients and Differential Equations written by john neuberger and published by Springer. This book was released on 2009-11-10 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Sobolev gradient of a real-valued functional on a Hilbert space is a gradient of that functional taken relative to an underlying Sobolev norm. This book shows how descent methods using such gradients allow a unified treatment of a wide variety of problems in differential equations. For discrete versions of partial differential equations, corresponding Sobolev gradients are seen to be vastly more efficient than ordinary gradients. In fact, descent methods with these gradients generally scale linearly with the number of grid points, in sharp contrast with the use of ordinary gradients. Aside from the first edition of this work, this is the only known account of Sobolev gradients in book form. Most of the applications in this book have emerged since the first edition was published some twelve years ago. What remains of the first edition has been extensively revised. There are a number of plots of results from calculations and a sample MatLab code is included for a simple problem. Those working through a fair portion of the material have in the past been able to use the theory on their own applications and also gain an appreciation of the possibility of a rather comprehensive point of view on the subject of partial differential equations.
Download or read book Sobolev Gradients and Differential Equations written by john neuberger and published by Springer. This book was released on 2006-11-13 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Sobolev gradient of a real-valued functional is a gradient of that functional taken relative to the underlying Sobolev norm. This book shows how descent methods using such gradients allow a unified treatment of a wide variety of problems in differential equations. Equal emphasis is placed on numerical and theoretical matters. Several concrete applications are made to illustrate the method. These applications include (1) Ginzburg-Landau functionals of superconductivity, (2) problems of transonic flow in which type depends locally on nonlinearities, and (3) minimal surface problems. Sobolev gradient constructions rely on a study of orthogonal projections onto graphs of closed densely defined linear transformations from one Hilbert space to another. These developments use work of Weyl, von Neumann and Beurling.
Download or read book Sobolev Gradients and Differential Equations written by John Neuberger and published by Springer Science & Business Media. This book was released on 2009-12-01 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Sobolev gradient of a real-valued functional on a Hilbert space is a gradient of that functional taken relative to an underlying Sobolev norm. This book shows how descent methods using such gradients allow a unified treatment of a wide variety of problems in differential equations. For discrete versions of partial differential equations, corresponding Sobolev gradients are seen to be vastly more efficient than ordinary gradients. In fact, descent methods with these gradients generally scale linearly with the number of grid points, in sharp contrast with the use of ordinary gradients. Aside from the first edition of this work, this is the only known account of Sobolev gradients in book form. Most of the applications in this book have emerged since the first edition was published some twelve years ago. What remains of the first edition has been extensively revised. There are a number of plots of results from calculations and a sample MatLab code is included for a simple problem. Those working through a fair portion of the material have in the past been able to use the theory on their own applications and also gain an appreciation of the possibility of a rather comprehensive point of view on the subject of partial differential equations.
Download or read book Sobolev gradients and differential equations written by John William Neuberger and published by . This book was released on 1997 with total page 149 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Sobolev Gradients and Differential Equations written by John W. Neuberger and published by . This book was released on 1997 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Sobolev gradient of a real-valued functional is a gradient of that functional taken relative to the underlying Sobolev norm. This book shows how descent methods using such gradients allow a unified treatment of a wide variety of problems in differential equations. Equal emphasis is placed on numerical and theoretical matters. Several concrete applications are made to illustrate the method. These applications include (1) Ginzburg-Landau functionals of superconductivity, (2) problems of transonic flow in which type depends locally on nonlinearities, and (3) minimal surface problems. Sobolev gradient constructions rely on a study of orthogonal projections onto graphs of closed densely defined linear transformations from one Hilbert space to another. These developments use work of Weyl, von Neumann and Beurling.
Download or read book Sobolev Gradient Methods written by Nauman Raza and published by LAP Lambert Academic Publishing. This book was released on 2010-08-01 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sobolev gradient methods resolve numerical difficulties in approximating solutions to differential equations and minima of error and energy functionals by construction of inner product spaces that one suitable for the problem at hand. The great efficiency achieved by setting the problem in right Sobolev space, makes steepest descent methods applicable to wide variety of problems. In this monograph, applications of Sobolev gradient methods in finite-difference and finite-element settings are considered for minimization of energy functionals, soliton solutions of the nonlinear Schrodinger equation, and pulse propagation through a fiber optic cable. For each problem, the practical application of the principle of selecting an appropriate Sobolev space setting is demonstrated. The advantages of the Sobolev gradient approach in efficiency and simplicity of implementation are shown. Engineers and computational physicists will find a clear description of the numerical method allowing immediate applications to problems of their interest.
Download or read book Using Gradient Descent Method to Solve Systems of Differential Equations Under to Sobolev Inner Product Space written by Jason A. Hatton and published by . This book was released on 2017 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Sobolev Spaces of Infinite Order and Differential Equations written by Julii A. Dubinskii and published by Springer Science & Business Media. This book was released on 1986-12-31 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Sobolev Spaces in Mathematics II written by Vladimir Maz'ya and published by Springer Science & Business Media. This book was released on 2008-11-26 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sobolev spaces become the established and universal language of partial differential equations and mathematical analysis. Among a huge variety of problems where Sobolev spaces are used, the following important topics are the focus of this volume: boundary value problems in domains with singularities, higher order partial differential equations, local polynomial approximations, inequalities in Sobolev-Lorentz spaces, function spaces in cellular domains, the spectrum of a Schrodinger operator with negative potential and other spectral problems, criteria for the complete integration of systems of differential equations with applications to differential geometry, some aspects of differential forms on Riemannian manifolds related to Sobolev inequalities, Brownian motion on a Cartan-Hadamard manifold, etc. Two short biographical articles on the works of Sobolev in the 1930s and the foundation of Akademgorodok in Siberia, supplied with unique archive photos of S. Sobolev are included.
Download or read book Gradient Inequalities written by Sen-Zhong Huang and published by American Mathematical Soc.. This book was released on 2006 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a survey of the relatively new research field of gradient inequalities and their applications. The exposition emphasizes the powerful applications of gradient inequalities in studying asymptotic behavior and stability of gradient-like dynamical systems. It explains in-depth how gradient inequalities are established and how they can be used to prove convergence and stability of solutions to gradient-like systems. This book will serve as an introduction for furtherstudies of gradient inequalities and their applications in other fields, such as geometry and computer sciences. This book is written for advanced graduate students, researchers and applied mathematicians interested in dynamical systems and mathematical modeling.
Download or read book Functional Analysis Sobolev Spaces and Partial Differential Equations written by Haim Brezis and published by Springer Science & Business Media. This book was released on 2010-11-02 with total page 600 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Elliptic Hyperbolic Partial Differential Equations written by Thomas H. Otway and published by Springer. This book was released on 2015-07-08 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text is a concise introduction to the partial differential equations which change from elliptic to hyperbolic type across a smooth hypersurface of their domain. These are becoming increasingly important in diverse sub-fields of both applied mathematics and engineering, for example: • The heating of fusion plasmas by electromagnetic waves • The behaviour of light near a caustic • Extremal surfaces in the space of special relativity • The formation of rapids; transonic and multiphase fluid flow • The dynamics of certain models for elastic structures • The shape of industrial surfaces such as windshields and airfoils • Pathologies of traffic flow • Harmonic fields in extended projective space They also arise in models for the early universe, for cosmic acceleration, and for possible violation of causality in the interiors of certain compact stars. Within the past 25 years, they have become central to the isometric embedding of Riemannian manifolds and the prescription of Gauss curvature for surfaces: topics in pure mathematics which themselves have important applications. Elliptic−Hyperbolic Partial Differential Equations is derived from a mini-course given at the ICMS Workshop on Differential Geometry and Continuum Mechanics held in Edinburgh, Scotland in June 2013. The focus on geometry in that meeting is reflected in these notes, along with the focus on quasilinear equations. In the spirit of the ICMS workshop, this course is addressed both to applied mathematicians and to mathematically-oriented engineers. The emphasis is on very recent applications and methods, the majority of which have not previously appeared in book form.
Download or read book Variational Methods Open Problems Recent Progress and Numerical Algorithms written by John Neuberger and published by American Mathematical Soc.. This book was released on 2004 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the conference on Variational Methods: Open Problems, Recent Progress, and Numerical Algorithms. It presents current research in variational methods as applied to nonlinear elliptic PDE, although several articles concern nonlinear PDE that are nonvariational and/or nonelliptic. The book contains both survey and research papers discussing important open questions and offering suggestions on analytical and numerical techniques for solving those open problems. It is suitable for graduate students and research mathematicians interested in elliptic partial differential equations.
Download or read book A Sequence of Problems on Semigroups written by john neuberger and published by Springer Science & Business Media. This book was released on 2011-09-15 with total page 131 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text consists of a sequence of problems which develop a variety of aspects in the field of semigroupsof operators. Many of the problems are not found easily in other books. Written in the Socratic/Moore method, this is a problem book without the answers presented. To get the most out of the content requires high motivation from the reader to work out the exercises. The reader is given the opportunity to discover important developments of the subject and to quickly arrive at the point of independent research. The compactness of the volume and the reputation of the author lends this consider set of problems to be a 'classic' in the making. This text is highly recommended for us as supplementary material for 3 graduate level courses.
Download or read book Pattern Recognition written by Rudolf Mester and published by Springer. This book was released on 2011-09-02 with total page 490 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 33rd Symposium of the German Association for Pattern Recognition, DAGM 2011, held in Frankfurt/Main, Germany, in August/September 2011. The 20 revised full papers and 22 revised poster papers were carefully reviewed and selected from 98 submissions. The papers are organized in topical sections on object recognition, adverse vision conditions challenge, shape and matching, segmentation and early vision, robot vision, machine learning, and motion. The volume also includes the young researcher's forum, a section where a carefully jury-selected ensemble of young researchers present their Master thesis work.
Download or read book Sobolev Spaces written by Vladimir Maz'ya and published by Springer. This book was released on 2013-12-21 with total page 506 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Sobolev spaces, i. e. the classes of functions with derivatives in L , occupy p an outstanding place in analysis. During the last two decades a substantial contribution to the study of these spaces has been made; so now solutions to many important problems connected with them are known. In the present monograph we consider various aspects of Sobolev space theory. Attention is paid mainly to the so called imbedding theorems. Such theorems, originally established by S. L. Sobolev in the 1930s, proved to be a useful tool in functional analysis and in the theory of linear and nonlinear par tial differential equations. We list some questions considered in this book. 1. What are the requirements on the measure f1, for the inequality q
Download or read book Recent Developments in Optimization Theory and Nonlinear Analysis written by Yair Censor and published by American Mathematical Soc.. This book was released on 1997 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the refereed proceedings of the special session on Optimization and Nonlinear Analysis held at the Joint American Mathematical Society-Israel Mathematical Union Meeting which took place at the Hebrew University of Jerusalem in May 1995. Most of the papers in this book originated from the lectures delivered at this special session. In addition, some participants who didn't present lectures and invited speakers who were unable to attend contributed their work. The fields of optimization theory and nonlinear analysis continue to be very active. This book presents not only the wide spectrum and diversity of the results, but also their manifold connections to other areas, such as differential equations, functional analysis, operator theory, calculus of variations, numerical analysis, and mathematical programming. In reading this book one encounters papers that deal, for example, with convex, quasiconvex and generalized convex functions, fixed and periodic points, fractional-linear transformations, moduli of convexity, monontone operators, Morse lemmas, Navier-Stokes equations, nonexpansive maps, nonsmooth analysis, numerical stability, products of projections, steepest descent, the Leray-Schauder degree, the turnpike property, and variational inequalities.