论文标题
对产品内核的Safronov-Dubovski凝结方程的质量保护解决方案的存在和独特性
Existence and Uniqueness of Mass Conserving Solutions to Safronov-Dubovski Coagulation Equation for Product Kernel
论文作者
论文摘要
本文介绍了产品合并系数的离散safronov-dubovski凝结方程的存在和大规模保存$ ϕ $，因此$ ϕ_ {i，j} \ j} \ leq ij $ \ forall $ $ $ $ $ $ $ $ $ i，j \ in \ mathbb {n} $保守和非保守截短系统都用于分析无限的ODES系统。在保守的情况下，Helly的选择定理用于证明全球存在，而对于非保守部分，我们利用DelaVallée-Poussin定理的精制版本来确定存在。此外，这表明这些溶液保留了密度。最后，当内核$ ϕ_ {i，j} \ leq \ text {min} \ {i^η，j^η\} $其中$η\ in [0,2] $时，这些解决方案被证明是唯一的。
The article presents the existence and mass conservation of solution for the discrete Safronov-Dubovski coagulation equation for the product coalescence coefficients $ϕ$ such that $ϕ_{i,j} \leq ij$ $\forall$ $i,j \in \mathbb{N}$. 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 $ϕ_{i,j} \leq \text{min}\{i^η,j^η\}$ where $η\in [0,2]$.
