论文标题
部分可观测时空混沌系统的无模型预测
Short Time Existence for Coupling of Scaled Mean Curvature Flow and Diffusion
论文作者
论文摘要
我们证明了由超出表面的几何演化方程组成的系统和抛物线方程组成的系统的短时间存在结果。更确切地说，我们讨论了一个平均曲率流量，该术语缩放的术语取决于在表面上定义的数量，该量与该数量的扩散方程相连。该证明是基于分裂的ANSATZ，使用线性化和收缩参数分别求解了两个方程。我们的结果是针对浸入式高空的情况下制定的，并在存在时间上产生均匀的下限，从而使高度函数的初始值发生很小的变化。
We prove a short time existence result for a system consisting of a geometric evolution equation for a hypersurface and a parabolic equation on this evolving hypersurface. More precisely, we discuss a mean curvature flow scaled with a term that depends on a quantity defined on the surface coupled to a diffusion equation for that quantity. The proof is based on a splitting ansatz, solving both equations separately using linearization and a contraction argument. Our result is formulated for the case of immersed hypersurfaces and yields a uniform lower bound on the existence time that allows for small changes in the initial value of the height function.
