论文标题
具有移动边界的非本地热方程
Non-local heat equations with moving boundary
论文作者
论文摘要
在本文中，我们考虑了时间增长的抛物线集中的非本地（时间）热方程，其边界由合适的曲线确定。我们为这些方程式提供了解决方案的概念，我们研究了域外的迪奇莱特条件下的适当性。证明了最大原则，并用于根据Dirichlet问题的最初基准来得出独特性和连续性。通过显示基于在边界上杀死的延迟的布朗尼运动的随机表示来证明存在。还获得了延迟的布朗运动及其交叉概率的几种相关分布特性。确定了该过程的均方根位移的渐近行为，表明扩散行为是异常的。
In this paper we consider non-local (in time) heat equations on time-increasing parabolic sets whose boundary is determined by a suitable curve. We provide a notion of solution for these equations and we study well-posedness under Dirichlet conditions outside the domain. A maximum principle is proved and used to derive uniqueness and continuity with respect to the initial datum of the solutions of the Dirichlet problem. Existence is proved by showing a stochastic representation based on the delayed Brownian motion killed on the boundary. Several related distributional properties of the delayed Brownian motion and its crossing probabilities are also obtained. The asymptotic behaviour of the mean square displacement of the process is determined, showing that the diffusive behaviour is anomalous.
