论文标题
固定液体中小颗粒运动的爱因斯坦模型：有限的繁殖速度
Einstein model of the movement of small particles in a stationary liquid revisited: Finite Propagation Speed
论文作者
论文摘要
前面提到的著名模型，尽管在随机过程中取得了突破，并且朝着布朗运动的构建迈出了巨大的一步，这导致了悖论：无限的繁殖速度和违反了热力学第二定律。我们通过假设颗粒浓度的扩散矩阵而不是恒定来适应模型，而不是恒定取决于爱因斯坦，并在假设有限的较小浓度扩散的假设下证明了有限的传播速度。该方法涉及以不同形式的非线性退化抛物线PDE，一种抛物线词，sobolev型不平等和Ladyzhenskaya-Aurtertseva迭代引理。
The aforementioned celebrated model, though a breakthrough in Stochastic processes and a great step toward the construction of the Brownian motion leads to a paradox: infinite propagation speed and violation of the 2nd law of thermodynamics. We adapt the model by assuming the diffusion matrix dependent of the concentration of particles, rather than constant it was up to Einstein, and prove a finite propagation speed under the assumption of a qualified decrease of the diffusion for small concentration. The method involves a nonlinear degenerated parabolic PDE in divergent form, a parabolic Sobolev-type inequality and the Ladyzhenskaya-Uraltseva iteration lemma.
