论文标题
一些非线性抛物线方程的缩放限制和随机均质化
Scaling limits and stochastic homogenization for some nonlinear parabolic equations
论文作者
论文摘要
本文的目的是双重的。首先是研究统计物理学中众所周知的Funaki-Spohn模型的抛物面缩放，连续和时空固定的渐近级别。在改变了随机扰动的热方程的未知数需要存在时空固定的永恒解决方案之后，该问题转变为均匀椭圆形的定性均质化，时空固定，差异形式，非线性偏差方程，这是本文的第二个目标。一个重要的步骤是构造无穷大时具有适当行为的校正器。
The aim of this paper is twofold. The first is to study the asymptotics of a parabolically scaled, continuous and space-time stationary in time version of the well-known Funaki-Spohn model in Statistical Physics. After a change of unknowns requiring the existence of a space-time stationary eternal solution of a stochastically perturbed heat equation, the problem transforms to the qualitative homogenization of a uniformly elliptic, space-time stationary, divergence form, nonlinear partial differential equation, the study of which is the second aim of the paper. An important step is the construction of correctors with the appropriate behavior at infinity.
