发表机构
Faculty of Advanced Science and Technology, Kumamoto University（熊本大学先进科学技术研究院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究无界曲面上扩散方程的稳定性与极大正则性，在无曲率假设下证明平缓斜率时存在全局强解并具$L^2$渐近稳定性，且在外力满足特定条件时推导极大正则性与Hölder连续性。
AI 中文摘要
本文研究了在无界曲面上、不对曲率作任何假设的扩散方程的稳定性与极大正则性。我们证明，当曲面斜率平缓时，曲面扩散系统存在唯一的全局强解，且满足$L^2$-渐近稳定性。当外力满足曲面散度形式和切向条件时，我们还推导了解的最大$L^2$-正则性。此外，我们研究了解关于时间的Hölder连续性。证明我们的稳定性和极大正则性结果的关键思想是利用Laplace算子和加权Laplace-Beltrami算子的良好性质，从而推导出无界曲面上Laplace-Beltrami算子的性质。
英文摘要
This paper studies both stability and maximal regularity of the diffusion equation on an unbounded surface without any assumptions on the curvature. We show that the surface diffusion system admits a unique global-in-time strong solution satisfying $L^2$-asymptotic stability when the slope of the surface is gentle. We also derive maximal $L^2$-regularity of the solution when the exterior force satisfies both surface divergence form and tangential condition. Moreover, we investigate the Hölder continuity with respect to time of the solution. The key idea of showing our stability and maximal regularity results is to apply nice properties of both Laplace and weighted Laplace-Beltrami operators in order to derive the properties of the Laplace-Beltrami operator on the unbounded surface.
Comments31 pages
