29th Article " The order of singularity of solutions for the stationary coagulation equation."

Nur fatmawati
16611047

The order of singularity of solutions for the stationary coagulation equation.

A models for particulate flows, where the disperse phase is made of particles subject to size variations. Are thus led to kinetic equations with coagulation and breakup operators, coupled to fluid mechanics equations. The existence and stability of stationary solutions. Also derive macroscopic models through asymptotic hydrodynamic regimes, once relevant scaling parameters have been identified.  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 W1,∞− regularity in space.