Functional Analysis and Applied Optimization in Banach Spaces Applications to Non-Convex Variational Models /

This 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...

Πλήρης περιγραφή

Λεπτομέρειες βιβλιογραφικής εγγραφής
Κύριος συγγραφέας: Botelho, Fabio (Συγγραφέας)
Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
Γλώσσα:English
Έκδοση: Cham : Springer International Publishing : Imprint: Springer, 2014.
Θέματα:
Διαθέσιμο Online:Full Text via HEAL-Link
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100 1 |a Botelho, Fabio.  |e author. 
245 1 0 |a Functional Analysis and Applied Optimization in Banach Spaces  |h [electronic resource] :  |b Applications to Non-Convex Variational Models /  |c by Fabio Botelho. 
264 1 |a Cham :  |b Springer International Publishing :  |b Imprint: Springer,  |c 2014. 
300 |a XVIII, 560 p. 57 illus., 51 illus. in color.  |b online resource. 
336 |a text  |b txt  |2 rdacontent 
337 |a computer  |b c  |2 rdamedia 
338 |a online resource  |b cr  |2 rdacarrier 
347 |a text file  |b PDF  |2 rda 
505 0 |a 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. 
520 |a This 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. 
650 0 |a Mathematics. 
650 0 |a Fourier analysis. 
650 0 |a Functional analysis. 
650 0 |a Functions of real variables. 
650 0 |a Numerical analysis. 
650 1 4 |a Mathematics. 
650 2 4 |a Functional Analysis. 
650 2 4 |a Real Functions. 
650 2 4 |a Fourier Analysis. 
650 2 4 |a Numerical Analysis. 
710 2 |a SpringerLink (Online service) 
773 0 |t Springer eBooks 
776 0 8 |i Printed edition:  |z 9783319060736 
856 4 0 |u http://dx.doi.org/10.1007/978-3-319-06074-3  |z Full Text via HEAL-Link 
912 |a ZDB-2-SMA 
950 |a Mathematics and Statistics (Springer-11649)