论文标题
汉密尔顿 - 雅各比 - 贝尔曼方程的庞大轮廓
The large time profile for Hamilton--Jacobi--Bellman equations
论文作者
论文摘要
在这里，我们研究了二阶汉密尔顿的cauchy问题粘度解决方案的巨大限制 - 雅各比 - 贝尔曼方程，带有凸汉密尔顿的汉密尔顿人。这个较大的限制解决了相应的固定问题，有时称为厄运问题。但是，这个问题具有多个粘度解决方案，因此，一个关键问题是这些解决方案中的哪些是由极限选择的。在这里，我们根据广义自动措施为库奇问题的粘度解决方案提供了一种表示。然后，我们使用此表示形式来表征初始数据和广义MATHER措施的较大时间限制。此外，我们对具有独立感兴趣的广义MATHER措施和二元定理建立了各种结果。
Here, we study the large-time limit of viscosity solutions of the Cauchy problem for second-order Hamilton--Jacobi--Bellman equations with convex Hamiltonians in the torus. This large-time limit solves the corresponding stationary problem, sometimes called the ergodic problem. This problem, however, has multiple viscosity solutions and, thus, a key question is which of these solutions is selected by the limit. Here, we provide a representation for the viscosity solution to the Cauchy problem in terms of generalized holonomic measures. Then, we use this representation to characterize the large-time limit in terms of the initial data and generalized Mather measures. In addition, we establish various results on generalized Mather measures and duality theorems that are of independent interest.
