On the Classical Limit of the Quantum Mechanics Based on the Hamilton-Jacobi Equation 从哈密顿-雅可毕方程看量子力学的经典极限
We prove that the value function is locally Lipschitz using observability inequalities and also characterize it as the unique positive viscosity solution of the corresponding Hamilton-Jacobi equation. 我们将运用观测不等式,证明值函数φ作为相应Hamilton-Jacobi方程的唯一粘性正解是局部Lipschitz连续的。
Hamilton-Jacobi equation in the spacetime of nonstationary Kerr black hole is studied by using a new tortoise coordinate transformation. It shows that the Hamilton-Jacobi equation can discuss not only the nonthermal radiation, but also the surface gravity of the black hole. 用一种新的tortoise坐标变换研究了动态Kerr黑洞时空中的HamiltonJacobi方程,其结果表明,根据HamiltonJacobi方程可以研究黑洞的量子非热辐射特征,也可以研究黑洞视界表面引力。
Finite element method and the finite difference approach are respectively applied to implement the numerical calculation of elastic equilibrium equation and Hamilton-Jacobi equation. The validity of the presented method is demonstrated by one typical example. 用有限元法和有限差分法相结合的方法分别实现弹性平衡方程和Hamilton-Jacobi方程的数值计算,并通过一个典型算例证明所研究方法的有效性。
The variations in Hamilton-Jacobi equation in curved spacetime are separated by means of tortoise coordinate transform. 适当地采用乌龟坐标变换,便可对弯曲时空中的Hamilton-Jacobi方程进行变量分离。
The computational efficiency could be saved without solving the complicated Hamilton-Jacobi equation, which was used in traditional level set method. 与传统水平集方法相比,不用求解复杂的Hamilton-Jacobi方程,提高了计算效率。
According to the Hamilton-Jacobi formulation of the Godunov's scheme, we study finite difference mothed for the propagation equation of non-ideal detonation in non-orthogonal body-fitted coordinate and present an algorithm. 根据Hamilton-Jacobi方程的Godunov差分格式,本文研究了非正交的贴体坐标系中非理想爆轰波传播方程的差分格式并提出了相应的数值方法。
The controller design need not solve any Hamilton-Jacobi equation. 控制器的设计不需要解任何HamiltonJacobi方程。
A Class of Difference Schemes with Staggered Grids for Hamilton-Jacobi Equation 一类求解Hamilton-Jacobi方程的交错网格差分格式
In Vaidya-Bonner-de Sitter black hole spacetime, the quantum nonthermal radiation and the horizon surface gravitation of black hole have been researched through studying Hamilton-Jacobi equation by using tortoise coordinate transformation. 在Vaidya-Bonner-DeSitter黑洞时空中,通过研究Hamilton-Jacobi方程,采用tortoise坐标变换,讨论了此黑洞的量子非热辐射及视界表面引力问题。
The minimum time function is lower semicontinuous and it is a viscosity supersolution to the contingent Hamilton-Jacobi equation. 极小时间函数是下半连续的且是相依Hamilton-Jacobi方程的粘性上解。
The quantum nonthermal radiation and the horizon surface gravitation of Dilaton-Maxwell black holes have been researched through studying Hamilton-Jacobi equation of particle movement. A new tortoise coordinate transformation is adopted in discussion. 通过研究在Dilaton-Maxwell黑洞时空中粒子运动的Hamilton-Jacobi方程,讨论了此黑洞的视界表面引力及量子非热辐射特征,其中采用了近来提出的新Tortoise坐标变换。
If the semi-discrete scheme among them is given more limitations, its numerical solution converges to the viscosity solution of Hamilton-Jacobi equation. 这些格式是TVD型的,在更强的条件下,其半离散格式的数值解收敛于Hamilton-Jacobi方程的粘性解。
Main Method of Nonconvex Hamilton-Jacobi Equation Using Flux Splitting 用通量分裂法解非凸Hamilton-Jacobi方程的主要算法
The temperature of black hole with an internal global monopole is studied by making use of generalized Tortoise coordinate conversion. Moreover, the quantum non-thermal radiation of the black hole is also studied from solving the Hamilton-Jacobi equation of particle in curved spacetime. 利用广义Tortoise坐标变换研究了含整体单极动态黑洞时空的温度,进而从解粒子在弯曲时空的哈密顿-雅可比方程出发研究了此黑洞的量子非热辐射。
The Hamilton-Jacobi Equation's Integrable Types Hamilton-Jacobi方程的可积情况
Then this chapter uses Hamilton-Jacobi equation to make dynamic control for the products 'pricing problem. Furthermore, the dynamic model is set up and relative property of the model is discussed. 提出使用Hamilton-Jacobi方程式来动态控制定价问题并且讨论模型的相关性质。
By the theory of segmenting first and then capturing being proposed, the failure of pretreatment to images with common scale values by Hamilton-Jacobi equation in original Zhu-Chan model is eliminated, from which Zhu-Chan model is extended. 提出先分割后捕捉的理论,解决了Zhu-Chan模型中用Hamilton-Jacobi方程对具有一般灰度的图像预处理失败的问题,扩大了模型的使用范围。
Compared with the simple Eikonal equation, the flux direction is implicitly dependent on the pedestrian density through an more complicated Hamilton-Jacobi equation at the time. 此时,对比于上面简单的Eikonal方程,流通量方向通过静态Hamilton-Jacobi方程隐式地依赖于行人流密度。
As a fully nonlinear partial differential equations, the classi-cal smooth solution of Hamilton-Jacobi equation is not easy to find or even not exist. 做为完全非线性的偏微分方程,Hamilton-Jacobi方程的经典光滑解不容易求出甚至不存在。