论文标题
在随机媒体中燃烧的长时间动力学
Long Time Dynamics for Combustion in Random Media
论文作者
论文摘要
我们研究了随机介质中燃烧过程的长时间动力学，以随机点火反应的反应扩散方程进行建模。人们期望在合理的假设上，这些方程式的解决方案的大时空尺度动力学几乎肯定受其他有效的PDE的控制，这应该是均质的汉密尔顿 - 雅各比方程。虽然以前在一个维度以及各个维度（即带有径向对称定律）中的各向同性反应证明了这一点，但我们在这里提供了这种现象的第一个证明，这是一般的非偶性多维环境中的第一个证明。我们的结果适用于具有有限依赖性范围的反应（即它们的值在空间中足够遥远的点上是独立的）以及一些具有无限依赖性范围的，并且基于证明这些反应中所有方向的确定性前沿（传播）速度的存在。
We study long time dynamics of combustive processes in random media, modeled by reaction-diffusion equations with random ignition reactions. One expects that under reasonable hypotheses on the randomness, large space-time scale dynamics of solutions to these equations is almost surely governed by a different effective PDE, which should be a homogeneous Hamilton-Jacobi equation. While this was previously proved in one dimension as well as for isotropic reactions in several dimensions (i.e., with radially symmetric laws), we provide here the first proof of this phenomenon in the general non-isotropic multidimensional setting. Our results hold for reactions that have finite ranges of dependence (i.e., their values are independent at sufficiently distant points in space) as well as for some with infinite ranges of dependence, and are based on proving existence of deterministic front (propagation) speeds in all directions for these reactions.
