Download or read book New Variational Principles for Systems of Partial Differential Equations written by John Richard Myers and published by . This book was released on 1972 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Variational Principles For Second order Differential Equations Application Of The Spencer Theory Of written by Joseph Grifone and published by World Scientific. This book was released on 2000-05-25 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt: The inverse problem of the calculus of variations was first studied by Helmholtz in 1887 and it is entirely solved for the differential operators, but only a few results are known in the more general case of differential equations. This book looks at second-order differential equations and asks if they can be written as Euler-Lagrangian equations. If the equations are quadratic, the problem reduces to the characterization of the connections which are Levi-Civita for some Riemann metric.To solve the inverse problem, the authors use the formal integrability theory of overdetermined partial differential systems in the Spencer-Quillen-Goldschmidt version. The main theorems of the book furnish a complete illustration of these techniques because all possible situations appear: involutivity, 2-acyclicity, prolongation, computation of Spencer cohomology, computation of the torsion, etc.

Download or read book Variational Principles for Second order Differential Equations written by J. Grifone and published by World Scientific. This book was released on 2000 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: The inverse problem of the calculus of variations was first studied by Helmholtz in 1887 and it is entirely solved for the differential operators, but only a few results are known in the more general case of differential equations. This book looks at second-order differential equations and asks if they can be written as Euler-Lagrangian equations. If the equations are quadratic, the problem reduces to the characterization of the connections which are Levi-Civita for some Riemann metric.To solve the inverse problem, the authors use the formal integrability theory of overdetermined partial differential systems in the Spencer-Quillen-Goldschmidt version. The main theorems of the book furnish a complete illustration of these techniques because all possible situations appear: involutivity, 2-acyclicity, prolongation, computation of Spencer cohomology, computation of the torsion, etc.

Download or read book Self dual Partial Differential Systems and Their Variational Principles written by Nassif Ghoussoub and published by Springer Science & Business Media. This book was released on 2008-11-11 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text is intended for a beginning graduate course on convexity methods for PDEs. The generality chosen by the author puts this under the classification of "functional analysis". The book contains new results and plenty of examples and exercises.

Download or read book The Variational Principles of Mechanics written by Cornelius Lanczos and published by Courier Corporation. This book was released on 2012-04-24 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: Philosophic, less formalistic approach to analytical mechanics offers model of clear, scholarly exposition at graduate level with coverage of basics, calculus of variations, principle of virtual work, equations of motion, more.

Download or read book Variational Methods written by Michael Struwe and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hilbert's talk at the second International Congress of 1900 in Paris marked the beginning of a new era in the calculus of variations. A development began which, within a few decades, brought tremendous success, highlighted by the 1929 theorem of Ljusternik and Schnirelman on the existence of three distinct prime closed geodesics on any compact surface of genus zero, and the 1930/31 solution of Plateau's problem by Douglas and Radò. The book gives a concise introduction to variational methods and presents an overview of areas of current research in this field. This new edition has been substantially enlarged, a new chapter on the Yamabe problem has been added and the references have been updated. All topics are illustrated by carefully chosen examples, representing the current state of the art in their field.

Download or read book Variational Problems in Materials Science written by Gianni Dal Maso and published by Springer Science & Business Media. This book was released on 2006-06-23 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the international workshop Variational Problems in Materials Science. Coverage includes the study of BV vector fields, path functionals over Wasserstein spaces, variational approaches to quasi-static evolution, free-discontinuity problems with applications to fracture and plasticity, systems with hysteresis or with interfacial energies, evolution of interfaces, multi-scale analysis in ferromagnetism and ferroelectricity, and much more.

Download or read book The Method of Weighted Residuals and Variational Principles written by Bruce A. Finlayson and published by SIAM. This book was released on 2013-12-30 with total page 429 pages. Available in PDF, EPUB and Kindle. Book excerpt: This classic book covers the solution of differential equations in science and engineering in such as way as to provide an introduction for novices before progressing toward increasingly more difficult problems. The Method of Weighted Residuals and Variational Principles describes variational principles, including how to find them and how to use them to construct error bounds and create stationary principles. The book also illustrates how to use simple methods to find approximate solutions, shows how to use the finite element method for more complex problems, and provides detailed information on error bounds. Problem sets make this book ideal for self-study or as a course text.

Download or read book Variational Methods in Nonconservative Phenomena written by B. D. Vujanovic and published by Academic Press. This book was released on 1989-05-01 with total page 383 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a comprehensive survey of analytic and approximate solutions of problems of applied mechanics, with particular emphasis on nonconservative phenomena. Include

Download or read book Partial Differential Equations with Variable Exponents written by Vicentiu D. Radulescu and published by CRC Press. This book was released on 2015-06-24 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: Partial Differential Equations with Variable Exponents: Variational Methods and Qualitative Analysis provides researchers and graduate students with a thorough introduction to the theory of nonlinear partial differential equations (PDEs) with a variable exponent, particularly those of elliptic type. The book presents the most important variational

Download or read book Dual Variational Principles for an Elliptic Partial Differential Equation written by J. Vacek and published by . This book was released on 1977 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book An Introduction to Modern Variational Techniques in Mechanics and Engineering written by Bozidar D. Vujanovic and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: * Atanackovic has good track record with Birkhauser: his "Theory of Elasticity" book (4072-X) has been well reviewed. * Current text has received two excellent pre-pub reviews. * May be used as textbook in advanced undergrad/beginning grad advanced dynamics courses in engineering, physics, applied math departments. *Also useful as self-study reference for researchers and practitioners. * Many examples and novel applications throughout. Competitive literature---Meirovich, Goldstein---is outdated and does not include the synthesis of topics presented here.

Download or read book Control Theory of Systems Governed by Partial Differential Equations written by A.K. Aziz and published by Academic Press. This book was released on 2014-05-10 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: Control Theory of Systems Governed by Partial Differential Equations covers the proceedings of the 1976 Conference by the same title, held at the Naval Surface Weapons Center, Silver Spring, Maryland. The purpose of this conference is to examine the control theory of partial differential equations and its application. This text is divided into five chapters that primarily focus on tutorial lecture series on the theory of optimal control of distributed systems. It describes the many manifestations of the theory and its applications appearing in the other chapters. This work also presents the principles of the duality and asymptotic methods in control theory, including the variational principle for the heat equation. A chapter highlights systems that are not of the linear quadratic type. This chapter also explores the control of free surfaces and the geometrical control variables. The last chapter provides a summary of the features and applications of the numerical approximation of problems of optimal control. This book will prove useful to mathematicians, engineers, and researchers.

Download or read book Variational Methods in Mathematical Physics written by Philippe Blanchard and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 419 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first edition (in German) had the prevailing character of a textbook owing to the choice of material and the manner of its presentation. This second (translated, revised, and extended) edition, however, includes in its new parts considerably more recent and advanced results and thus goes partially beyond the textbook level. We should emphasize here that the primary intentions of this book are to provide (so far as possible given the restrictions of space) a selfcontained presentation of some modern developments in the direct methods of the cal culus of variations in applied mathematics and mathematical physics from a unified point of view and to link it to the traditional approach. These modern developments are, according to our background and interests: (i) Thomas-Fermi theory and related theories, and (ii) global systems of semilinear elliptic partial-differential equations and the existence of weak solutions and their regularity. Although the direct method in the calculus of variations can naturally be considered part of nonlinear functional analysis, we have not tried to present our material in this way. Some recent books on nonlinear functional analysis in this spirit are those by K. Deimling (Nonlinear Functional Analysis, Springer, Berlin Heidelberg 1985) and E. Zeidler (Nonlinear Functional Analysis and Its Applications, Vols. 1-4; Springer, New York 1986-1990).

Download or read book Variational Topological and Partial Order Methods with Their Applications written by Zhitao Zhang and published by Springer Science & Business Media. This book was released on 2012-09-17 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear functional analysis is an important branch of contemporary mathematics. It's related to topology, ordinary differential equations, partial differential equations, groups, dynamical systems, differential geometry, measure theory, and more. In this book, the author presents some new and interesting results on fundamental methods in nonlinear functional analysis, namely variational, topological and partial order methods, which have been used extensively to solve existence of solutions for elliptic equations, wave equations, Schrödinger equations, Hamiltonian systems etc., and are also used to study the existence of multiple solutions and properties of solutions. This book is useful for researchers and graduate students in the field of nonlinear functional analysis.

Download or read book Invariant Variational Principles written by Logan and published by Academic Press. This book was released on 1978-02-22 with total page 189 pages. Available in PDF, EPUB and Kindle. Book excerpt: Invariant Variational Principles

Download or read book Nonlinear Partial Differential Equations for Scientists and Engineers written by Lokenath Debnath and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 602 pages. Available in PDF, EPUB and Kindle. Book excerpt: This expanded and revised second edition is a comprehensive and systematic treatment of linear and nonlinear partial differential equations and their varied applications. Building upon the successful material of the first book, this edition contains updated modern examples and applications from diverse fields. Methods and properties of solutions, along with their physical significance, help make the book more useful for a diverse readership. The book is an exceptionally complete text/reference for graduates, researchers, and professionals in mathematics, physics, and engineering.