Abstract

In the paper, the Cauchy problem for wave equations with constant and variable coefficients is considered. We assume that the initial data are a random function with finite mean energy density and study the convergence of distributions of the solutions to a limiting Gaussian measure for large times. We derive the formulas for the limiting energy current density (in mean) and find a new class of stationary nonequilibrium states for the studied model.

中文翻译：

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波动方程的平稳非平衡测度

摘要

在本文中，考虑了具有固定系数和可变系数的波动方程的柯西问题。我们假设初始数据是一个具有有限平均能量密度的随机函数，并研究了有限高斯测度的解的分布的收敛性。我们推导了极限能量电流密度（均值）的公式，并为研究的模型找到了一类新的稳态非平衡态。