Rigorous Numerical Verification of Uniqueness and Smoothness in a Surface Growth Model
Rigorous Numerical Verification of Uniqueness and Smoothness in a Surface Growth Model
复制标题
DOI：
10.1016/j.jmaa.2015.04.025
复制
发表时间：
2013-11
期刊：
影响因子：
--
通讯作者：
D. Blomker;Christian Nolde;James C. Robinson
中科院分区：
文献类型：
--
作者：
D. Blomker;Christian Nolde;James C. Robinson
基于数值数据和后验分析，对于某些分析方法失败的初始数据，我们严格验证了标量表面生长模型的全局解的唯一性和平滑性，该模型与 3D 纳维-斯托克斯方程具有惊人的相似性。关键点是控制解范数的标量 ODE 的推导，其系数取决于数值数据。我们没有明确求解该 ODE，而是探索了三种不同的数值方法，为其解决方案提供了严格的上限。
Based on numerical data and a-posteriori analysis we verify rigorously the uniqueness and smoothness of global solutions to a scalar surface growth model with striking similarities to the 3D Navier–Stokes equations, for certain initial data for which analytical approaches fail. The key point is the derivation of a scalar ODE controlling the norm of the solution, whose coefficients depend on the numerical data. Instead of solving this ODE explicitly, we explore three different numerical methods that provide rigorous upper bounds for its solution.