论文标题
折扣汉密尔顿 - 雅各比方程的平滑亚树种
Smooth subsolutions of the discounted Hamilton-Jacobi equations
论文作者
论文摘要
对于打折的汉密尔顿 - 雅各比方程，$$λu+h（x，d_x u）= 0，\ x \ in m，$$我们构造$ c^{1,1} $ subsolutions，实际上是投影的aubry集中的解决方案。在额外的双曲线假设下，可以改善此类种植的平滑度。作为应用程序，我们可以使用此类种植措施来识别相关的合成式流动的最大全局吸引子，并控制Lax-Oleinik Semogroups的收敛速度
For the discounted Hamilton-Jacobi equation,$$λu+H(x,d_x u)=0, \ x \in M, $$we construct $C^{1,1}$ subsolutions which are indeed solutions on the projected Aubry set. The smoothness of such subsolutions can be improved under additional hyperbolicity assumptions. As applications, we can use such subsolutions to identify the maximal global attractor of the associated conformally symplectic flow and to control the convergent speed of the Lax-Oleinik semigroups
