Title: On the space-time analyticity of the inhomogeneous heat equation on the half space with Neumann boundary conditions Show Chinese title

Title: 非齐次热方程在具有 Neumann 边界条件的半空间上的时空解析性

Abstract: We consider the inhomogeneous heat equation on the half-space $\mathbb R_{+}^{d}$ with Neumann boundary conditions. We prove a space-time Gevrey regularity of the solution, with a radius of analyticity uniform up to the boundary of the half-space. We also address the case of homogeneous Robin boundary conditions. Our results generalize the case of homogeneous Dirichlet boundary conditions established by Kukavica and Vicol in [10]. Show Chinese abstract

Abstract: 我们考虑半空间$\mathbb R_{+}^{d}$上的非齐次热方程，具有诺伊曼边界条件。 我们证明了解的空间-时间盖尔德雷正则性，解析半径在半空间边界附近是统一的。 我们还讨论了齐次罗宾边界条件的情况。 我们的结果推广了 Kukavica 和 Vicol 在 [10] 中建立的齐次狄利克雷边界条件的情况。