2021/05/22 by Ya-Nan Wang, Jun Yan, Wang, Ya-Nan +3
Computer Science · Engineering · Physics and Astronomy · #35B40 #37J50 #37J55 #49L25 #Analysis of PDEs (math.AP) #Dynamical Systems (math.DS) #FOS: Mathematics #Nonlinear Dynamics and Pattern Formation #Quantum chaos and dynamical systems #Stability and Controllability of Differential Equations
paper · pdf · doi:10.48550/arxiv.2105.10667
openalex publication_date 2021/05/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this article we develop an analogue of Aubry Mather theory for time periodic dissipative equation \ \beginaligned xamp;=∂p H(x,p,t),
pamp;=-∂x H(x,p,t)-f(t)p \endaligned . with (x,p,t)∈ T^*M×\mathbb T (compact manifold M without boundary). We discuss the asymptotic behaviors of viscosity solutions of associated Hamilton-Jacobi equation ∂t u+f(t)u+H(x,∂x u,t)=0, (x,t)∈ M×\mathbb T w.r.t. certain parameters, and analyze the meanings in controlling the global dynamics. We also discuss the prospect of applying our conclusions to many physical models.