论文标题
贝克里 - ÉmeryRicci曲率条件下的热方程式的时间分析性
Time analyticity for the heat equation under Bakry-Émery Ricci curvature condition
论文作者
论文摘要
Inspired by Hongjie Dong and Qi S. Zhang's article \cite{ZQ2}, we find that the analyticity in time for a smooth solution of the heat equation with exponential quadratic growth in the space variable can be extended to any complete noncompact Riemannian manifolds with Bakry-Émery Ricci curvature bounded below and the potential function being of at most quadratic growth.因此，我们的结果适用于所有梯度RICCI孤子。作为推论，我们在具有相似生长条件的一类函数中，对向后热方程的溶解度提供了必要的条件。此外，我们还考虑了在[2，+\ infty）$中的某些$ l^p $空间中的解决方案，并证明其在时间上的分析性。
Inspired by Hongjie Dong and Qi S. Zhang's article \cite{ZQ2}, we find that the analyticity in time for a smooth solution of the heat equation with exponential quadratic growth in the space variable can be extended to any complete noncompact Riemannian manifolds with Bakry-Émery Ricci curvature bounded below and the potential function being of at most quadratic growth. Therefore, our result holds on all gradient Ricci solitons. As a corollary, we give a necessary and sufficient condition on the solvability of the backward heat equation in a class of functions with the similar growth condition. In addition, we also consider the solution in certain $L^p$ spaces with $p\in[2,+\infty)$ and prove its analyticity with respect to time.
