论文标题
分数边界价值问题和弹性粘性布朗尼动作，ii：有限域
Fractional Boundary Value Problems and elastic sticky Brownian motions, II: The bounded domain
论文作者
论文摘要
有限域上的粘性扩散过程在边界给出的较低维空间上花费有限的时间（和有限的平均时间）。一旦该过程撞到边界，就会在随机量后重新开始。在边界上，它可以根据与内部不同的动态保持或移动。此类过程的特征是出现在管理问题的边界条件下的时间衍生。我们使用通过合适过程的右插入获得的时间变化，以描述分数粘性条件和相关的边界行为。我们获得了分数边界值问题（涉及分数动态边界条件）会导致粘性扩散，将无限的平均时间（和有限时间）花在较低维度的边界上。在宏观的角度，这种行为可以与陷阱效应相关联。
Sticky diffusion processes on bounded domains spend finite time (and finite mean time) on the lower-dimensional space given by the boundary. Once the process hits the boundary, then it starts again after a random amount of time. While on the boundary it can stay or move according to dynamics that are different from those in the interior. Such processes may be characterized by a time-derivative appearing in the boundary condition for the governing problem. We use time changes obtained by right-inverses of suitable processes in order to describe fractional sticky conditions and the associated boundary behaviours. We obtain that fractional boundary value problems (involving fractional dynamic boundary conditions) lead to sticky diffusions spending an infinite mean time (and finite time) on a lower-dimensional boundary. Such a behaviour can be associated with a trap effect in the macroscopic point of view.
