Local well posedness for a linear coagulation equation

In this paper we derive some a priori estimates for a class of linear coagulation equations with particle fluxes towards large size particles. The derived estimates allow us to prove local well posedness for the considered equations. Some regularizing effects exhibited by the equations in the particle distributions for large particle sizes are discussed in detail.Comment: 71 page

Optimal bounds for self-similar solutions to coagulation equations with product kernel

We consider mass-conserving self-similar solutions of Smoluchowski's coagulation equation with multiplicative kernel of homogeneity $2l\lambda \in (0,1)$. We establish rigorously that such solutions exhibit a singular behavior of the form $x^{-(1+2\lambda)}$ as $x \to 0$. This property had been conjectured, but only weaker results had been available up to now