AI 中文总结
本文针对ℝ上分子束外延的表面生长模型，证明倒抛物线为稳定定态解，其小扰动按O(t⁻¹/² log t)速率衰减，该结果部分解释相邻岛合并现象。
AI 中文摘要
针对ℝ上分子束外延下的表面生长模型，我们证明倒抛物线是稳定定态解，即其任意小扰动以O(t⁻¹/² log t)的速率在L^∞(ℝ)中衰减。该证明基于线性化扰动方程生成的显式解算子。此结果部分解释了两个相邻岛合并为更大岛的现象，且对于足够小的初始数据，其解的任意导数均在L²(ℝ)中衰减。
英文摘要
For the surface growth model under molecular beam epitaxy on $\mathbb{R}$, we show that an inverted parabola is a stable steady solution in the sense that any small perturbation of it decays in $L^{\infty}(\mathbb{R})$ at the rate $O(t^{-1/2}\log t)$. The proof is based on the explicit solution operator generated by the linearized perturbation equation. This result partially justifies the merging of two neighboring islands into a bigger one. Moreover, any derivative of its solution is shown to be decaying in $L^{2}(\mathbb{R})$ for sufficiently small initial data.
Comments17 pages, 4 figures
