Behavior of solutions of the coagulation equation for the limited uniform coagulation kernel

Applying a limiter function with respect to the ratio of the volumes of colliding particles to the coagulation kernel a new family of kernels arises. The behavior of the solutions of the coagulation equation for the simplest member of this family (the so-called Π-kernel), is examined in the present work using several mathematical tools. It is shown that even this kernel exhibits zero order homogeneity, self-similar solutions of the coagulation equation do not exist. Surprisingly enough, even a slight change to the constant coagulation kernel induces a fundamental change to the nature of the coagulation equation solution.