论文标题
随机时间分数扩散和波动方程以及逆随机源问题的适应性良好
Well-posedness of the stochastic time-fractional diffusion and wave equations and inverse random source problems
论文作者
论文摘要
在本文中，我们关注的是希尔伯特空间中的随机时间裂缝扩散波。本文的主要目的是建立初始有限价值问题的随机弱解的特性，例如存在，唯一性和规律性估计。此外，我们将获得的理论应用于逆源问题。在边界测量下，这个反问题的独特性已证明。
In this paper, we are concerned with the stochastic time-fractional diffusion-wave equations in a Hilbert space. The main objective of this paper is to establish properties of the stochastic weak solutions of the initial-boundary value problem, such as the existence, uniqueness and regularity estimates. Moreover, we apply the obtained theories to an inverse source problem. The uniqueness of this inverse problem under the boundary measurements is proved.
