Variational principle for contact Hamiltonian systems and its applications

DOI10.1016/J.MATPUR.2018.08.011zbMath1409.37064arXiv1702.04451OpenAlexW2950813907WikidataQ129333820 ScholiaQ129333820MaRDI QIDQ1726949

Lin Wang, Jun Yan, Kaizhi Wang

Publication date: 20 February 2019

Published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1702.04451

zbMATH Keywords

viscosity solutionsfirst-order PDEscontact Hamilton's equationsimplicit variational principle

Mathematics Subject Classification ID

Variational methods for problems in mechanics (70G75) Nonlinear first-order PDEs (35F20) Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games (49L25) Contact systems (37J55)

Related Items (30)

Viscosity subsolutions of Hamilton–Jacobi equations and invariant sets of contact Hamilton systems ⋮ Hamilton–Jacobi equations with their Hamiltonians depending Lipschitz continuously on the unknown ⋮ The Aubry set and Mather set in the embedded contact Hamiltonian system ⋮ Existence of solutions to contact mean-field games of first order ⋮ Orbital dynamics on invariant sets of contact Hamiltonian systems ⋮ Representation formulas for contact type Hamilton-Jacobi equations ⋮ Multiple asymptotic behaviors of solutions in the generalized vanishing discount problem ⋮ Convergence of solutions of Hamilton-Jacobi equations depending nonlinearly on the unknown function ⋮ A variational principle for contact Hamiltonian systems ⋮ Contact extension and symplectification ⋮ Local strict singular characteristics. II: Existence for stationary equations on \(\mathbb{R}^2\) ⋮ Time periodic solutions of Hamilton-Jacobi equations with autonomous Hamiltonian on the circle ⋮ Periodic dynamics of a class of non-autonomous contact Hamiltonian systems ⋮ Herglotz' variational principle and Lax-Oleinik evolution ⋮ Stability and weak KAM solutions of contact Hamilton-Jacobi equation ⋮ Parameterized viscosity solutions of convex Hamiltonian systems with time periodic damping ⋮ Resonance conjecture via weak KAM theory ⋮ Viscosity solutions of contact Hamilton-Jacobi equations with Hamiltonians depending periodically on unknown functions ⋮ Unnamed Item ⋮ Vanishing contact structure problem and convergence of the viscosity solutions ⋮ Aubry-Mather theory for contact Hamiltonian systems ⋮ Convergence of the viscosity solution of non-autonomous Hamilton-Jacobi equations ⋮ Weak KAM solutions of Hamilton-Jacobi equations with decreasing dependence on unknown functions ⋮ On the vanishing discount problem from the negative direction ⋮ A representation formula of viscosity solutions to weakly coupled systems of Hamilton-Jacobi equations with applications to regularizing effect ⋮ Generalized ergodic problems: existence and uniqueness structures of solutions ⋮ Weak KAM theory for action minimizing random walks ⋮ Aubry-Mather theory for contact Hamiltonian systems. II ⋮ On the dynamics of contact Hamiltonian systems: I. Monotone systems ⋮ Finite-time convergence of solutions of Hamilton-Jacobi equations

Cites Work

• Unnamed Item
• Unnamed Item
• An Introduction to the Theory of Viscosity Solutions for First-Order Hamilton–Jacobi Equations and Applications
• Implicit variational principle for contact Hamiltonian systems
• Viscosity Solutions of Hamilton-Jacobi Equations
• Théorème KAM faible et théorie de Mather sur les systèmes lagrangiens

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