Self-dual Partial Differential Systems and Their Variational Principles

• Main Author: Ghoussoub, Nassif (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: New York, NY : Springer New York, 2009.
• Series: Springer Monographs in Mathematics,
• Subjects: Mathematics.; Information technology.; Business > Data processing.; Functional analysis.; Partial differential equations.; Functional Analysis.; Partial Differential Equations.; IT in Business.

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 cont...

Table of Contents:

• 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.