Viscosity solutions of Hamilton-Jacobi equations, and asymptotics for Hamiltonian systems
Viscosity solutions of Hamilton-Jacobi equations, and asymptotics for Hamiltonian systems
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Hamilton-Jacobi 方程的粘度解和哈密顿系统的渐近
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发表时间：
2002
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通讯作者：
D. Gomes
中科院分区：
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作者：
D. Gomes
抽象的。在本文中，我们应用哈密顿-雅可比方程的粘度解理论来理解某些哈密顿流的结构。特别是，我们描述了最小化轨道的渐近行为，并证明了经典哈密尔顿-雅可比可积理论的类似物在非常一般的条件下成立。然后，将偏微分方程技术与动力系统思想（Mather测度、遍历性）相结合，研究与时间无关的Hamilton-Jacobi方程的解，即一致连续性、差商和非唯一性。
Abstract. In this paper we apply the theory of viscosity solutions of Hamilton-Jacobi equations to understand the structure of certain Hamiltonian flows. In particular, we describe the asymptotic behavior of minimizing orbits, and prove analogs of the classical Hamilton-Jacobi integrability theory that hold under very general conditions. Then, combining partial differential equations techniques with dynamical systems ideas (Mather measures, ergodicity) we study solutions of time-independent Hamilton-Jacobi equation, namely, uniform continuity, difference quotients and non-uniqueness.