Behavior of solutions of the coagulation equation for the limited uniform coagulation kernel
Abstract 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 P 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.