论文标题
使用非保守近似的存在和密度保护
Existence and density conservation using a non-conservative approximation for Safronov-Dubovski aggregation equation
论文作者
论文摘要
本文介绍了Safronov-dubovski方程的全球存在和密度保护，用于三个不同的系数$ ϕ $，使得$ ϕ_ {i，j} \ leq \ frac \ frac {（i+j）} {\ min \ min \ min \ min \ \ {i，j \ \} $，$，$，$，$ j; $ ϕ_ {i，j} \ leq（1+i+j）^α$ $ \ forall $ $ i，j \ in \ mathbb {n} $，$α\ in [0,1] $。应用了非保守近似来研究问题，并实施了诸如Helly的选择定理和DelaVallée-Poussin定理的精制版本之类的结果，以确定每种核的存在。该文章还重点介绍了这种方程式的每单位量质量量的条件。
The paper deals with the global existence and density conservation for the Safronov-Dubovski equation for three different coefficients $ϕ$ such that $ϕ_{i,j} \leq \frac{(i+j)}{\min\{i,j\}}$, $ϕ_{i,j} \leq (i+j)$ and $ϕ_{i,j} \leq (1+i+j)^α$ $\forall$ $i,j \in \mathbb{N}$, $α\in [0,1]$. 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 Vallée-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.
