Periodic solutions of the Hamilton-Jacobi equation with a periodic non-homogeneous term and Aubry-Mather theory
Periodic solutions of the Hamilton-Jacobi equation with a periodic non-homogeneous term and Aubry-Mather theory
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具有周期性非齐次项的 Hamilton-Jacobi 方程的周期解和 Aubry-Mather 理论
DOI：
10.1070/sm1999v190n10abeh000435
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发表时间：
1999
影响因子：
0.8
通讯作者：
A. Sobolevskiĭ
中科院分区：
文献类型：
--
作者：
A. Sobolevskiĭ
证明了具有周期非齐次项的一维Hamilton-Jacobi方程有一系列广义解，每个广义解都可以表示为线性函数和周期函数之和；这种解的唯一性条件是根据奥布里-马瑟理论给出的。
It is proved that the one-dimensional Hamilton-Jacobi equation with a periodic non-homogeneous term admits a family of generalized solutions, each of which can be represented as the sum of a linear and a periodic function; a condition for the uniqueness of such a solution is given in terms of Aubry-Mather theory.