标题： 随机斯特凡问题在移动超曲面上：通过非齐次单调性新框架的方法 显示英文标题

标题： Stochastic Stefan problem on moving hypersurfaces: an approach by a new framework of nonhomogeneous monotonicity

摘要： 本文的目的是在移动超曲面上建立随机Stefan问题的适定性。 通过一个特别设计的变换，结果表明我们需要在固定超曲面上求解具有新型非齐次单调性的随机偏微分方程，该单调性涉及一族时间依赖算子。 这类新的SPDEs具有独立的研究价值，也可以用于求解许多其他有趣的模型，例如随机$p$-拉普拉斯方程、随机Allen-Cahn方程以及随机热方程在时间依赖域或超曲面上的问题。 （单调）算子值微积分和移动超曲面的几何分析在研究中起着重要作用。 此外，关于随机二维Navier-Stokes方程在移动域上的适定性的未来结果也基于我们的框架。 显示英文摘要

摘要： The purpose of this paper is to establish the well-posedness of the stochastic Stefan problem on moving hypersurfaces. Through a specially designed transformation, it turns out we need to solve stochastic partial differential equations on a fixed hypersurface with a new kind of nonhomogeneous monotonicity involving a family of time-dependent operators. This new class of SPDEs is of independent interest and can also be applied to solve many other interesting models such as the stochastic $p$-Laplacian equations, stochastic Allen-Cahn equation and stochastic heat equations on time-dependent domains or hypersurfaces. (Monotone) Operator-valued calculus and geometric analysis of moving hypersurfaces play important roles in the study. Moreover, a forthcoming result on the well-posedness of stochastic 2D Navier-Stokes equation on moving domains is also based on our framework.