论文标题
2D晶格的宏观波传播，随机质量
Macroscopic Wave Propagation for 2D Lattice with Random Masses
论文作者
论文摘要
我们认为具有随机，独立和相同分布质量的简单二维谐波晶格。使用随机均质化的方法，我们表明具有长波初始数据的解决方案以适当的含义收敛于有效波动方程的溶液。融合很强，几乎是确定的。此外，讨论了晶格维度在收敛速率中的作用。该技术结合了能量估计以及有关下高斯随机变量的强大经典结果。
We consider a simple two-dimemsional harmonic lattice with random, independent and identically distributed masses. Using the methods of stochastic homogenization, we show that solutions with long wave initial data converge in an appropriate sense to solutions of an effective wave equation. The convergence is strong and almost sure. In addition, the role of the lattice's dimension in the rate of convergence is discussed. The technique combines energy estimates with powerful classical results about sub-Gaussian random variables.
