{
  "id": "2105.10667",
  "version": "v1",
  "published": "2021-05-22T09:01:55.000Z",
  "updated": "2021-05-22T09:01:55.000Z",
  "title": "Parameterized viscosity solutions of convex Hamiltonian systems with time periodic damping",
  "authors": [
    "Ya-Nan Wang",
    "Jun Yan",
    "Jianlu Zhang"
  ],
  "comment": "40pages,3 figures",
  "categories": [
    "math.DS",
    "math.AP"
  ],
  "abstract": "In this article we develop an analogue of Aubry Mather theory for time periodic dissipative equation \\[ \\left\\{ \\begin{aligned} \\dot x&=\\partial_p H(x,p,t),\\\\ \\dot p&=-\\partial_x H(x,p,t)-f(t)p \\end{aligned} \\right. \\] with $(x,p,t)\\in T^*M\\times\\mathbb T$ (compact manifold $M$ without boundary). We discuss the asymptotic behaviors of viscosity solutions of associated Hamilton-Jacobi equation \\[ \\partial_t u+f(t)u+H(x,\\partial_x u,t)=0,\\quad(x,t)\\in M\\times\\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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-05-22T09:01:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B40",
      "37J50",
      "37J55",
      "49L25"
    ],
    "keywords": [
      "convex hamiltonian systems",
      "parameterized viscosity solutions",
      "time periodic damping",
      "aubry mather theory",
      "time periodic dissipative equation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 40,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}