Generalized Moment Method for Smoluchowski Coagulation Equation and Mass Conservation Property

In this paper, we develop a generalized moment method with a continuous weight function for the Smoluchowski coagulation equation in its continuous form to study the mass conservation property of this equation. We first establish some basic inequalities for the generalized moment and prove the mass conservation property under a sufficient condition on the kernel and an initial condition, utilizing these inequalities. Additionally, we provide some concrete examples of coagulation kernels that exhibit mass conservation properties and show that these kernels exhibit either polynomial or exponential growth along specific particular curves.

Automated summary

In this paper, a generalized moment method with a continuous weight function is developed to study the mass conservation property of the Smoluchowski coagulation equation in its continuous form. Basic inequalities for the generalized moment are established and used to prove the mass conservation property under certain conditions on the kernel and initial condition. Concrete examples of coagulation kernels that exhibit mass conservation properties and demonstrate polynomial or exponential growth along specific curves are provided.