论文标题
存在动态的低级别近似与抛物线问题
Existence of dynamical low-rank approximations to parabolic problems
论文作者
论文摘要
显示了两个空间维度中抛物线偏微分方程动力学低级别进化问题的弱解决方案的存在和唯一性，还涵盖了椭圆形部分中的非二元分节扩散。该证明基于低级别歧管上的各种时间步变方案。此外，该方案被证明与计算这种低级别进化的实用方法密切相关。
The existence and uniqueness of weak solutions to dynamical low-rank evolution problems for parabolic partial differential equations in two spatial dimensions is shown, covering also non-diagonal diffusion in the elliptic part. The proof is based on a variational time-stepping scheme on the low-rank manifold. Moreover, this scheme is shown to be closely related to practical methods for computing such low-rank evolutions.
