The Inverse Problem of the Calculus of Variations
The Inverse Problem of the Calculus of Variations

Author: Dmitry V. Zenkov

Publisher: Springer

Published: 2015-10-15

Total Pages: 296

ISBN-13: 9462391092

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The aim of the present book is to give a systematic treatment of the inverse problem of the calculus of variations, i.e. how to recognize whether a system of differential equations can be treated as a system for extremals of a variational functional (the Euler-Lagrange equations), using contemporary geometric methods. Selected applications in geometry, physics, optimal control, and general relativity are also considered. The book includes the following chapters: - Helmholtz conditions and the method of controlled Lagrangians (Bloch, Krupka, Zenkov) - The Sonin-Douglas's problem (Krupka) - Inverse variational problem and symmetry in action: The Ostrogradskyj relativistic third order dynamics (Matsyuk.) - Source forms and their variational completion (Voicu) - First-order variational sequences and the inverse problem of the calculus of variations (Urban, Volna) - The inverse problem of the calculus of variations on Grassmann fibrations (Urban).

New Prospects in Direct, Inverse and Control Problems for Evolution Equations
New Prospects in Direct, Inverse and Control Problems for Evolution Equations

Author: Angelo Favini

Publisher: Springer

Published: 2014-11-27

Total Pages: 472

ISBN-13: 3319114069

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This book, based on a selection of talks given at a dedicated meeting in Cortona, Italy, in June 2013, shows the high degree of interaction between a number of fields related to applied sciences. Applied sciences consider situations in which the evolution of a given system over time is observed, and the related models can be formulated in terms of evolution equations (EEs). These equations have been studied intensively in theoretical research and are the source of an enormous number of applications. In this volume, particular attention is given to direct, inverse and control problems for EEs. The book provides an updated overview of the field, revealing its richness and vitality.

The Calculus of Variations
The Calculus of Variations

Author: Bruce van Brunt

Publisher: Springer Science & Business Media

Published: 2006-04-18

Total Pages: 295

ISBN-13: 0387216979

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Suitable for advanced undergraduate and graduate students of mathematics, physics, or engineering, this introduction to the calculus of variations focuses on variational problems involving one independent variable. It also discusses more advanced topics such as the inverse problem, eigenvalue problems, and Noether’s theorem. The text includes numerous examples along with problems to help students consolidate the material.

Introduction To The Calculus of Variations And Its Applications, Second Edition
Introduction To The Calculus of Variations And Its Applications, Second Edition

Author: Frederic Wan

Publisher: CRC Press

Published: 1995-01-01

Total Pages: 660

ISBN-13: 9780412051418

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This comprehensive text provides all information necessary for an introductory course on the calculus of variations and optimal control theory. Following a thorough discussion of the basic problem, including sufficient conditions for optimality, the theory and techniques are extended to problems with a free end point, a free boundary, auxiliary and inequality constraints, leading to a study of optimal control theory.

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Author: V. M. Filippov

Publisher: American Mathematical Soc.

Published: 1989-12-31

Total Pages: 260

ISBN-13: 9780821898246

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This book develops a variational method for solving linear equations with $B$-symmetric and $B$-positive operators and generalizes the method to nonlinear equations with nonpotential operators. The author carries out a constructive extension of the variational method to ``nonvariational'' equations (including parabolic equations) in classes of functionals which differ from the Euler-Lagrange functionals. In this connection, some new functions spaces are considered. Intended for mathematicians working in the areas of functional analysis and differential equations, this book would also prove useful for researchers in other areas and students in advanced courses who use variational methods in solving linear and nonlinear boundary value problems in continuum mechanics and theoretical physics.