标题： 确定性增长模型的收敛性 显示英文标题

标题： Convergence of deterministic growth models

摘要： 我们证明了大量确定性生长模型的缩放高度在空间和时间上的均匀收敛性，这些模型是单调的，并且在常数平移下保持不变。 极限被表征为一阶或二阶偏微分方程的唯一（粘性解），这取决于生长模型是按双曲方式还是抛物方式缩放。 这些结果大大简化并扩展了第一作者最近的工作，使其适用于更一般的表面生长模型。 证明基于Barles和第二作者开发的方法论，以证明近似方案的收敛性。 显示英文摘要

摘要： We prove the uniform in space and time convergence of the scaled heights of large classes of deterministic growth models that are monotone and equivariant under translations by constants. The limits are characterized as the unique (viscosity solutions) of first- or second-order partial differential equations depending on whether the growth models are scaled hyperbolically or parabolically. The results greatly simplify and extend a recent work by the first author to more general surface growth models. The proofs are based on the methodology developed by Barles and the second author to prove convergence of approximation schemes.