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In this paper we give a global existence and uniqueness theorem for aninitial and boundary value problem (IBVP) relative to the coagulation equationof water droplets and we show the convergence of the global solution to thestationary solution. The coagulation equation is an integro-differentialequation that describes the variation of the density $\sigma$ of water dropletsin the atmosphere. Furthermore, IBVP is considered on a strip limited by twohorizontal planes and its boundary condition is such that rain fall from thestrip. To obtain this result of global existence of the solution $\sigma$ inthe space of bounded continuous functions, through the method ofcharacteristics, we assume bounded continuous and small data, whereas thevector field, besides being bounded continuous, has $W^{1,\infty}-$ regularityin space.

Global solution for the coagulation equation of water droplets in atmosphere between two horizontal planes