The Action Principle and Partial Differential Equations. (AM-146), Volume 146 /

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 differen...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Christodoulou, Demetrios (Autor)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Princeton, NJ : Princeton University Press, [2016]
Colección:Annals of Mathematics Studies ; 146
Temas:
Differential equations, Hyperbolic.
Symplectic manifolds.
MATHEMATICS / Differential Equations / Partial.
Action (physics).
Boundary value problem.
Canonical form.
Causal structure.
Classical mechanics.
Complex analysis.
Configuration space.
Conservative vector field.
Conserved current.
Conserved quantity.
Continuum mechanics.
Derivative.
Diffeomorphism.
Differentiable manifold.
Differential geometry.
Dimension.
Dimensional analysis.
Dirichlet's principle.
Einstein field equations.
Electromagnetic field.
Equation.
Equations of motion.
Equivalence class.
Error term.
Euclidean space.
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.
Fiber bundle.
Foliation.
Fritz John.
General relativity.
Hamiltonian mechanics.
Hamilton-Jacobi equation.
Harmonic map.
Hessian matrix.
Holomorphic function.
Hyperbolic partial differential equation.
Hyperplane.
Hypersurface.
Identity element.
Iteration.
Iterative method.
Lagrangian (field theory).
Lagrangian.
Legendre transformation.
Lie algebra.
Linear approximation.
Linear differential equation.
Linear map.
Linear span.
Linearity.
Linearization.
Maximum principle.
Maxwell's equations.
Nonlinear system.
Open set.
Ordinary differential equation.
Orthogonal complement.
Parameter.
Partial differential equation.
Phase space.
Pointwise.
Poisson bracket.
Polynomial.
Principal part.
Principle of least action.
Probability.
Pullback bundle.
Pullback.
Quadratic form.
Quantity.
Requirement.
Riemannian manifold.
Second derivative.
Simultaneous equations.
Special case.
State function.
Stokes' theorem.
Subset.
Surjective function.
Symplectic geometry.
Tangent bundle.
Tangent vector.
Theorem.
Theoretical physics.
Theory.
Underdetermined system.
Variable (mathematics).
Vector bundle.
Vector field.
Vector space.
Volume form.
Zero of a function.
Zero set.
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