We present the analysis of advection-diffusion equations with random coefficients on moving hypersurfaces. We define weak and strong material derivative, that take into account also the spacial movement. Then we define the solution space for these kind of equations, which is the Bochner-type space of random functions defined on moving domain. Under suitable regularity assumptions we prove the existence and uniqueness of solutions of the concerned equation, and also we give some regularity results about the solution.

中文翻译：

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演化超曲面上具有随机系数的对流扩散方程

我们提出了对移动超曲面上具有随机系数的对流扩散方程的分析。我们定义了弱和强材料衍生物，这也考虑了空间运动。然后我们定义这类方程的解空间，即定义在移动域上的随机函数的Bochner 型空间。在适当的正则性假设下，证明了有关方程解的存在唯一性，并给出了该解的一些正则性结果。