两水平面间大气中水滴凝结方程的整体解
Global solution for the coagulation equation of water droplets in atmosphere between two horizontal planes
摘要：
本文给出了水滴凝聚方程的初边值问题整体解的存在唯一性定理，并证明了整体解收敛于定常解.凝结方程是描述大气中水滴密度$σ$变化的积分微分方程。此外，IBVP被认为是一个由两个水平面限制的带，其边界条件是这样的，降雨从带。为了得到解$σ$在有界连续函数空间中整体存在的结果，我们通过特征线方法，假设有界连续和小数据，而向量场除了是有界连续的之外，在空间中还具有$W^{1,\infty}-$正则性.
英文摘要：
In this paper we give a global existence and uniqueness theorem for an initial and boundary value problem (IBVP) relative to the coagulation equation of water droplets and we show the convergence of the global solution to the stationary solution. The coagulation equation is an integro-differential equation that describes the variation of the density $σ$ of water droplets in the atmosphere. Furthermore, IBVP is considered on a strip limited by two horizontal planes and its boundary condition is such that rain fall from the strip. To obtain this result of global existence of the solution $σ$ in the space of bounded continuous functions, through the method of characteristics, we assume bounded continuous and small data, whereas the vector field, besides being bounded continuous, has $W^{1,\infty}-$ regularity in space.
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