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Stability of solutions to contact Hamilton-Jacobi equation on the circle (2401.14679v1)
Published 26 Jan 2024 in math.AP and math.DS
Abstract: Combing the weak KAM method for contact Hamiltonian systems and the theory of viscosity solutions for Hamilton-Jacobi equations, we study the Lyapunov stability and instability of viscosity solutions for evolutionary contact Hamilton-Jacobi equation in the first part. In the second part, we study the existence and multiplicity of time-periodic solutions.
- M. Bardi and I. Capuzzo-Dolcetta. Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations. Systems and Control: Foundations & Applications. Birkhäuser Boston Inc., 1997.
- P. Cannarsa and C. Sinestrari. Semiconcave functions, Hamilton-Jacobi equations, and optimal control, volume 58 of Progress in Nonlinear Differential Equations and their Applications. Birkhäuser Boston, Inc., Boston, MA, 2004.
- Viscosity solutions of Hamilton-Jacobi equations. Trans. Amer. Math. Soc., 277(1):1–42, 1983.
- A. Fathi. Weak KAM theorem in Lagrangian dynamics. Cambridge University Press, Cambridge.
- H. Ishii. Asymptotic solutions for large time of Hamilton-Jacobi equations: International Congress of Mathematicians. Eur. Math. Soc., 3:213–227, 2006.
- Hamilton–Jacobi equations with their Hamiltonians depending lipschitz continuously on the unknown. Communications in Partial Differential Equations, 47(2):417–452, 02 2022.
- P.-L. Lions. Generalized solutions of Hamilton-Jacobi equations, volume 69 of Research Notes in Mathematics. Pitman (Advanced Publishing Program), Boston, Mass.-London, 1982.
- Homogenization of Hamilton-Jacobi equations. unpublished work, 1987.
- R. Mañé. Generic properties and problems of minimizing measures of Lagrangian systems. Nonlinearity, 9(2):273–310, 1996.
- H. V. Tran. Hamilton-Jacobi equations: Theory and applications, volume 213. American Mathematical Soc., 2021.
- Implicit variational principle for contact Hamiltonian systems. Nonlinearity, 30(2):492–515, 2017.
- Aubry–Mather Theory for Contact Hamiltonian Systems. Comm. Math. Phys., 366(3):981–1023, 2019.
- Variational principle for contact Hamiltonian systems and its applications. J. Math. Pures Appl., 123(9):167–200, 2019.
- Weak KAM solutions of Hamilton-Jacobi equations with decreasing dependence on unknown functions. Journal of Differential Equations, 286:411–432, 2021.
- Time periodic solutions of hamilton-jacobi equations with autonomous hamiltonian on the circle. Journal de Mathématiques Pures et Appliquées, 171:122–141, 2023.
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