Existence and Uniqueness of Mass Conserving Solutions to Safronov-Dubovski Coagulation Equation for Product Kernel

Abstract

The article presents the existence and mass conservation of solution for the discrete Safronov-Dubovski coagulation equation for the product coalescence coefficients $\varphi$ such that ${\varphi }_{i,j}\le ij$ $\forall$ $i,j\in \mathbb{N}$. Both conservative and non-conservative truncated systems are used to analyse the infinite system of ODEs. In the conservative case, Helly's selection theorem is used to prove the global existence while for the non-conservative part, we make use of the refined version of De la Vallée-Poussin theorem to establish the existence. Further, it is shown that these solutions conserve density. Finally, the solutions are shown to be unique when the kernel ${\varphi }_{i,j}\le \text{min}\{i^{\eta },j^{\eta }\}$ where $\eta \in [0,2]$.

arXiv commentThere are some technical issues