Existence and density conservation using a non-conservative approximation for Safronov-Dubovski aggregation equation

Abstract

The paper deals with the global existence and density conservation for the Safronov-Dubovski equation for three different coefficients $\phi$ such that $\phi_{i,j} \leq \frac{(i+j)}{\min\{i,j\}}$, $\phi_{i,j} \leq (i+j)$ and $\phi_{i,j} \leq (1+i+j)^{\alpha}$ $\forall$ $i,j \in \mathbb{N}$, $\alpha \in [0,1]$. The non-conservative approximation is applied to study the problem and results such as Helly's selection theorem and the refined version of the De la Vall\'ee-Poussin theorem are implemented to establish the existence of each case of the kernel. The article also focuses on the conditions for the conservation of mass per unit volume for such an equation.