Action Principle and Partial Differential Equations
Regular price
€107.99
14 days return policy
Shipping & Delivery
A01=Demetrios Christodoulou
Action (physics)
Author_Demetrios Christodoulou
Boundary value problem
Category=PBKJ
Causal structure
Classical mechanics
Configuration space
Conservative vector field
Conserved quantity
Continuum mechanics
Diffeomorphism
Differentiable manifold
Differential geometry
Dimensional analysis
Dirichlet's principle
Einstein field equations
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Equation
Equations of motion
Euler system
Euler's equations (rigid body dynamics)
Euler-Lagrange equation
Existence theorem
Existential quantification
Exponential map (Lie theory)
Exponential map (Riemannian geometry)
Exterior derivative
General relativity
Hamilton-Jacobi equation
Hamiltonian mechanics
Harmonic map
Hessian matrix
Holomorphic function
Hyperbolic partial differential equation
Hypersurface
Identity element
Iterative method
Lagrangian
Lagrangian (field theory)
Lie algebra
Linear approximation
Linear map
Linearity
Linearization
Maximum principle
Maxwell's equations
Nonlinear system
Ordinary differential equation
Orthogonal complement
Partial differential equation
Phase space
Poisson bracket
Polynomial
Principal part
Pullback
Pullback bundle
Quadratic form
Riemannian manifold
Second derivative
Simultaneous equations
Special case
Stokes' theorem
Surjective function
Symplectic geometry
Tangent bundle
Tangent vector
Theorem
Theoretical physics
Theory
Variable (mathematics)
Vector bundle
Vector field
Volume form
Product details
- ISBN 9780691049571
- Weight: 454g
- Dimensions: 197 x 254mm
- Publication Date: 17 Jan 2000
- Publisher: Princeton University Press
- Publication City/Country: US
- Product Form: Paperback
Secure
checkout
Fast Shipping
Easy returns
This book introduces new methods in the theory of partial differential equations derivable from a Lagrangian. These methods constitute, in part, an extension to partial differential equations of the methods of symplectic geometry and Hamilton-Jacobi theory for Lagrangian systems of ordinary differential equations. A distinguishing characteristic of this approach is that one considers, at once, entire families of solutions of the Euler-Lagrange equations, rather than restricting attention to single solutions at a time. The second part of the book develops a general theory of integral identities, the theory of "compatible currents," which extends the work of E. Noether. Finally, the third part introduces a new general definition of hyperbolicity, based on a quadratic form associated with the Lagrangian, which overcomes the obstacles arising from singularities of the characteristic variety that were encountered in previous approaches. On the basis of the new definition, the domain-of-dependence theorem and stability properties of solutions are derived. Applications to continuum mechanics are discussed throughout the book.
The last chapter is devoted to the electrodynamics of nonlinear continuous media.
Demetrios Christodoulou is Professor of Mathematics at Princeton University. He has been awarded a John and Catherine MacArthur Fellowship, as well as a John Simon Guggenheim Fellowship. His previous book The Global Nonlinear Stability of the Minkowski Space (Princeton), cowritten with Sergiu Klainerman, won the Bücher Memorial Prize of the American Mathematical Society.
