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OverviewThis book introduces the basic concepts of real and functional analysis. It presents the fundamentals of the calculus of variations, convex analysis, duality, and optimization that are necessary to develop applications to physics and engineering problems. The book includes introductory and advanced concepts in measure and integration, as well as an introduction to Sobolev spaces. The problems presented are nonlinear, with non-convex variational formulation. Notably, the primal global minima may not be attained in some situations, in which cases the solution of the dual problem corresponds to an appropriate weak cluster point of minimizing sequences for the primal one. Indeed, the dual approach more readily facilitates numerical computations for some of the selected models. While intended primarily for applied mathematicians, the text will also be of interest to engineers, physicists, and other researchers in related fields. Full Product DetailsAuthor: Fabio BotelhoPublisher: Springer International Publishing AG Imprint: Springer International Publishing AG Edition: Softcover reprint of the original 1st ed. 2014 Dimensions: Width: 15.50cm , Height: 3.10cm , Length: 23.50cm Weight: 8.891kg ISBN: 9783319382067ISBN 10: 3319382063 Pages: 560 Publication Date: 23 August 2016 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: Manufactured on demand We will order this item for you from a manufactured on demand supplier. Table of Contents 1. Topological Vector Spaces.- 2. The Hahn-Bananch Theorems and Weak Topologies.- 3. Topics on Linear Operators.- 4. Basic Results on Measure and Integration.- 5. The Lebesgue Measure in Rn.- 6. Other Topics in Measure and Integration.- 7. Distributions.- 8. The Lebesque and Sobolev Spaces.- 9. Basic Concepts on the Calculus of Variations.- 10. Basic Concepts on Convex Analysis.- 11. Constrained Variational Analysis.- 12. Duality Applied to Elasticity.- 13. Duality Applied to a Plate Model.- 14. About Ginzburg-Landau Type Equations: The Simpler Real Case.- 15. Full Complex Ginzburg-Landau System.- 16. More on Duality and Computation in the Ginzburg-Landau System.- 17. On Duality Principles for Scalar and Vectorial Multi-Well Variational Problems.- 18. More on Duality Principles for Multi-Well Problems.- 19. Duality and Computation for Quantum Mechanics Models.- 20. Duality Applied to the Optimal Design in Elasticity.- 21. Duality Applied to Micro-magnetism.- 22. The Generalized Method of Lines Applied to Fluid Mechanics.- 23. Duality Applied to the Optimal Control and Optimal Design of a Beam Model.ReviewsThe aim of the present book is to consider a variety of problems arising in applications in relation with non-convex variational models. ... The book will be a valuable resource for students and researchers in applied mathematics, physics, mechanics, and engineering. (Jan Lovisek, Mathematical Reviews, August, 2015) Author InformationTab Content 6Author Website:Countries AvailableAll regions |