An ergodic control problem arising from the principal eigenfunction of an elliptic operator
An ergodic control problem arising from the principal eigenfunction of an elliptic operator
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由椭圆算子主本征函数引起的遍历控制问题
DOI：
10.2969/jmsj/04310049
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发表时间：
1991
影响因子：
0.7
通讯作者：
H. Nagai
中科院分区：
文献类型：
--
作者：
A. Bensoussan;H. Nagai
考虑二阶拟线性偏微分方程：-1/2Δvα+H（x，α vα）αvα=0，其中非线性项H（x，α vα）在α vα上二次增长，α为正常数.在遍历控制问题中，研究了有界区域上具有周期或Neumann边界条件的这类方程，研究了当α趋于0时解vα的渐近性态。在本文中，我们将上述方程专门化到H（x，λ vα）=1/2的情况|α| 2 -V（x），但把它放在整个欧氏空间Rn上
Let us consider the following second order quasi-linear partial differential equation: -1/2Δvα+H(x,⊇vα)αvα=0 with a quadratic growth nonlinear term H(x,⊇vα) on ⊇vα, where α is a positive constant. Such kinds of equations on bounded regions with periodic or Neumann boundary conditions have been studied in connection with ergodic control problems, where the asymptotic behaviour of the solution vα as α tends to 0 is investigated. In the present article we specialize the equation above to the case where H(x,⊇vα)=1/2|⊇vα| 2 -V(x) but treat it on whole Euclidean space R n