关于Lifshitz-Slyozov-Wagner Ostwald熟化理论中的初值问题
On the initial-value problem in the Lifshitz-Slyozov-Wagner theory of Ostwald ripening
摘要：
奥斯特瓦尔德熟化的LSW理论关注的是通过具有共同平均场的扩散质量传递而演化的稀颗粒系统的尺寸分布的时间演化。我们证明了具有粒子大小紧支撑的测度值解的整体存在性、唯一性和对初值的连续依赖性。这些结果是建立相对于一个自然的拓扑空间的大小分布，一个给定的Wasserstein度量，测量最小的最大体积变化所需的重新安排一个分布到另一个。
英文摘要：
The LSW theory of Ostwald ripening concerns the time evolution of the size distribution of a dilute system of particles that evolve by diffusional mass transfer with a common mean field. We prove global existence, uniqueness and continuous dependence on initial data for measure-valued solutions with compact support in particle size. These results are established with respect to a natural topology on the space of size distributions, one given by the Wasserstein metric which measures the smallest maximum volume change required to rearrange one distribution into another.
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