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Self-dual Partial Differential Systems and Their Variational Principles / by Nassif Ghoussoub
Contributor(s): Resource type: Ressourcentyp: Buch (Online)Book (Online)Language: English Series: Springer Monographs in Mathematics | SpringerLink BücherPublisher: New York, NY : Springer New York, 2009Description: Online-Ressource (digital)ISBN:- 9780387848976
- 515.353
- 515.7
- QA319-329.9
- QA374
Contents:
Summary: Convex Analysis on Phase Space -- Legendre-Fenchel Duality on Phase Space -- Self-dual Lagrangians on Phase Space -- Skew-Adjoint Operators and Self-dual Lagrangians -- Self-dual Vector Fields and Their Calculus -- Completely Self-Dual Systems and their Lagrangians -- Variational Principles for Completely Self-dual Functionals -- Semigroups of Contractions Associated to Self-dual Lagrangians -- Iteration of Self-dual Lagrangians and Multiparameter Evolutions -- Direct Sum of Completely Self-dual Functionals -- Semilinear Evolution Equations with Self-dual Boundary Conditions -- Self-Dual Systems and their Antisymmetric Hamiltonians -- The Class of Antisymmetric Hamiltonians -- Variational Principles for Self-dual Functionals and First Applications -- The Role of the Co-Hamiltonian in Self-dual Variational Problems -- Direct Sum of Self-dual Functionals and Hamiltonian Systems -- Superposition of Interacting Self-dual Functionals -- Perturbations of Self-Dual Systems -- Hamiltonian Systems of Partial Differential Equations -- The Self-dual Palais-Smale Condition for Noncoercive Functionals -- Navier-Stokes and other Self-dual Nonlinear Evolutions.Summary: Based on recent research by the author and his graduate students, this text describes novel variational formulations and resolutions of a large class of partial differential equations and evolutions, many of which are not amenable to the methods of the classical calculus of variations. While it contains many new results, the general and unifying framework of the approach, its versatility in solving a disparate set of equations, and its reliance on basic functional analytic principles, makes it suitable for an intermediate level graduate course. The applications, however, require a fair knowledge of classical analysis and PDEs which is needed to make judicious choices of function spaces where the self-dual variational principles need to be applied. It is the author's hope that this material will become standard for all graduate students interested in convexity methods for PDEs. Nassif Ghoussoub is a Distinguished University Professor at the University of British Columbia. He was editor-in-chief of the Canadian Journal of Mathematics for the period 1993-2003, and has served on the editorial board of various international journals. He is the founding director of the Pacific Institute for the Mathematical Sciences (PIMS), and a co-founder of the MITACS Network of Centres of Excellence. He is also the founder and scientific director of the Banff International Research Station (BIRS). He is the recipient of many awards, including the Coxeter-James, and the Jeffrey-Williams prizes. He was elected Fellow of the Royal Society of Canada in 1993, and was the recipient of a Doctorat Honoris Causa from the Universite Paris-Dauphine in 2004.PPN: PPN: 1647563895Package identifier: Produktsigel: ZDB-2-SEB | ZDB-2-SXMS | ZDB-2-SMA
""Preface""; ""Contents""; ""Chapter 1 Introduction""; ""Part I CONVEX ANALYSIS ON PHASE SPACE""; ""Chapter 2 Legendre-Fenchel Duality on Phase Space""; ""Chapter 3 Self-dual Lagrangians on Phase Space""; ""Chapter 4 Skew-Adjoint Operators and Self-dual Lagrangians""; ""Chapter 5 Self-dual Vector Fields and Their Calculus""; ""Part II COMPLETELY SELF-DUAL SYSTEMS AND THEIR LAGRANGIANS""; ""Chapter 6 Variational Principles for Completely Self-dual Functionals""; ""Chapter 7 Semigroups of Contractions Associated to Self-dual Lagrangians""
""Chapter 8 Iteration of Self-dual Lagrangians and Multiparameter Evolutions""""Chapter 9 Direct Sum of Completely Self-dual Functionals""; ""Chapter 10 Semilinear Evolution Equations with Self-dual Boundary Conditions""; ""Part III SELF-DUAL SYSTEMS AND THEIR ANTISYMMETRIC HAMILTONIANS""; ""Chapter 11 The Class of Antisymmetric Hamiltonians""; ""Chapter 12 Variational Principles for Self-dual Functionals and First Applications""; ""Chapter 13 The Role of the Co-Hamiltonian in Self-dual Variational Problems""; ""Chapter 14 Direct Sum of Self-dual Functionals and Hamiltonian Systems""
""Chapter 15 Superposition of Interacting Self-dual Functionals""""Part IV PERTURBATIONS OF SELF-DUAL SYSTEMS""; ""Chapter 16 Hamiltonian Systems of Partial Differential Equations""; ""Chapter 17 The Self- dual Palais-Smale Condition for Noncoercive Functionals""; ""Chapter 18 Navier-Stokes and other Self-dual Nonlinear Evolutions""; ""References""; ""Index""
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