论文标题
对离散碰撞引起的破裂方程和解决方案的各种特性的适应性良好
Well-posedness to the discrete collision-induced breakage equation and various properties of solutions
论文作者
论文摘要
研究了非线性碰撞引起的断裂方程的离散版本。研究解决方案的存在已针对一系列无限的碰撞核和女儿分布功能，碰撞内核$ a_ {i，j} $满足$ a_ {i，j} \ j} \ leq a i j $ for某些$ a> 0 $。更确切地说，事实证明，在适当的条件下，始终存在至少一个质量持续的解决方案。在合理的一般条件下，还证明了解决方案独特性的结果。此外，建立了矩，不同的性能和解决方案的持续依赖性的传播，以及某些不变特性和解决方案的较大时间行为。
A discrete version of the nonlinear collision-induced breakage equation is studied. Existence of solutions is investigated for a broad class of unbounded collision kernels and daughter distribution functions, the collision kernel $a_{i,j}$ satisfiying $a_{i,j} \leq A i j$ for some $A>0$. More precisely, it is proved that given suitable conditions, there exists at least one mass-conserving solution for all times. A result on the uniqueness of solutions is also demonstrated under reasonably general conditions. Furthermore, the propagation of moments, differentiability, and the continuous dependence of solutions are established, along with some invariance properties and the large-time behaviour of solutions.
