Variational Principles For Second Order Differential Equations

Author : Joseph Grifone
Publisher : World Scientific
ISBN 13 : 9814495360
Total Pages : 228 pages
Book Rating : 4.63/5 ( download)

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Download or read book Variational Principles for Second-Order Differential Equations written by Joseph Grifone and published by World Scientific. This book was released on 2000-05-25 with total page 228 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. Contents:An Introduction to Formal Integrability Theory of Partial Differential SystemsFrölicher–Nijenhuis Theory of DerivationsDifferential Algebraic Formalism of ConnectionsNecessary Conditions for Variational SpraysObstructions to the Integrability of the Euler–Lagrange SystemThe Classification of Locally Variational Sprays on Two-Dimensional ManifoldsEuler–Lagrange Systems in the Isotropic Case Readership: Mathematicians. Keywords:Calculus of Variations;Inverse Problem;Euler-Lagrange Equation;Sprays;Formal Integrability;Involution;Janet-Riquier Theory;Spencer TheoryReviews: “Everybody seriously interested in the modern theory of the inverse problem of the calculus of variations should take a look at this book.” Zentralblatt MATH

Author : William B. Gordon
Publisher :
ISBN 13 :
Total Pages : 16 pages
Book Rating : 4.86/5 ( download)

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Download or read book Jacobian Variational Principles and the Equivalence of Second Order Systems written by William B. Gordon and published by . This book was released on 1972 with total page 16 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : J. Grifone
Publisher : World Scientific
ISBN 13 : 9789810237349
Total Pages : 236 pages
Book Rating : 4.40/5 ( download)

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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.

Author : A. M. Arthurs
Publisher : Oxford University Press, USA
ISBN 13 :
Total Pages : 172 pages
Book Rating : 4.39/5 ( download)

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Download or read book Complementary Variational Principles written by A. M. Arthurs and published by Oxford University Press, USA. This book was released on 1980 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Bruce A. Finlayson
Publisher : SIAM
ISBN 13 : 1611973244
Total Pages : 429 pages
Book Rating : 4.42/5 ( download)

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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.

Author : Vojislav Maric
Publisher : Springer
ISBN 13 : 3540465200
Total Pages : 141 pages
Book Rating : 4.01/5 ( download)

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Download or read book Regular Variation and Differential Equations written by Vojislav Maric and published by Springer. This book was released on 2007-05-06 with total page 141 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first book offering an application of regular variation to the qualitative theory of differential equations. The notion of regular variation, introduced by Karamata (1930), extended by several scientists, most significantly de Haan (1970), is a powerful tool in studying asymptotics in various branches of analysis and in probability theory. Here, some asymptotic properties (including non-oscillation) of solutions of second order linear and of some non-linear equations are proved by means of a new method that the well-developed theory of regular variation has yielded. A good graduate course both in real analysis and in differential equations suffices for understanding the book.

Author : Dazhong Lao
Publisher : Springer Nature
ISBN 13 : 9811560706
Total Pages : 1006 pages
Book Rating : 4.05/5 ( download)

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Download or read book Fundamental Theories and Their Applications of the Calculus of Variations written by Dazhong Lao and published by Springer Nature. This book was released on 2020-09-02 with total page 1006 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on the calculus of variations, including fundamental theories and applications. This textbook is intended for graduate and higher-level college and university students, introducing them to the basic concepts and calculation methods used in the calculus of variations. It covers the preliminaries, variational problems with fixed boundaries, sufficient conditions of extrema of functionals, problems with undetermined boundaries, variational problems of conditional extrema, variational problems in parametric forms, variational principles, direct methods for variational problems, variational principles in mechanics and their applications, and variational problems of functionals with vector, tensor and Hamiltonian operators. Many of the contributions are based on the authors’ research, addressing topics such as the extension of the connotation of the Hilbert adjoint operator, definitions of the other three kinds of adjoint operators, the extremum function theorem of the complete functional, unified Euler equations in variational methods, variational theories of functionals with vectors, modulus of vectors, arbitrary order tensors, Hamiltonian operators and Hamiltonian operator strings, reconciling the Euler equations and the natural boundary conditions, and the application range of variational methods. The book is also a valuable reference resource for teachers as well as science and technology professionals.

Author : Avner Friedman
Publisher :
ISBN 13 :
Total Pages : 728 pages
Book Rating : 4.10/5 ( download)

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Download or read book Variational Principles and Free-boundary Problems written by Avner Friedman and published by . This book was released on 1988 with total page 728 pages. Available in PDF, EPUB and Kindle. Book excerpt: This advanced graduate-level text examines variational methods in partial differential equations and illustrates their applications to a number of free-boundary problems. Detailed statements of the standard theory of elliptic and parabolic operators make this treatment readable for engineers, students, and nonspecialists alike. The text's first two chapters can be used for a single-semester graduate course in variational inequalities or partial differential equations. The succeeding chapters -- covering jets and cavities, variational problems with potentials, and free-boundary problems not in variational form -- are more specialized and self-contained. Readers who have mastered chapters 1 and 2 will be able to conduct research on the problems explored in subsequent chapters. Bibliographic remarks conclude each chapter, along with several problems and exercises.

Author : Gianni Dal Maso
Publisher : Springer Science & Business Media
ISBN 13 : 3764375655
Total Pages : 166 pages
Book Rating : 4.52/5 ( download)

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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.

Author : Richard S. Palais
Publisher : American Mathematical Soc.
ISBN 13 : 0821821385
Total Pages : 329 pages
Book Rating : 4.81/5 ( download)

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Download or read book Differential Equations, Mechanics, and Computation written by Richard S. Palais and published by American Mathematical Soc.. This book was released on 2009-11-13 with total page 329 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a conceptual introduction to the theory of ordinary differential equations, concentrating on the initial value problem for equations of evolution and with applications to the calculus of variations and classical mechanics, along with a discussion of chaos theory and ecological models. It has a unified and visual introduction to the theory of numerical methods and a novel approach to the analysis of errors and stability of various numerical solution algorithms based on carefully chosen model problems. While the book would be suitable as a textbook for an undergraduate or elementary graduate course in ordinary differential equations, the authors have designed the text also to be useful for motivated students wishing to learn the material on their own or desiring to supplement an ODE textbook being used in a course they are taking with a text offering a more conceptual approach to the subject.