一类离散的非线性爆炸方程平衡点的稳定性

Stability of Equilibria to a Class of Discrete Nonlinear Breakage Equations

本文所研究的非线性爆炸方程实质上是由可数无穷多个彼此相互关联的非线性常微分方程所组成的自治系统 ,它刻划了在只有基本粒子与 i-粒子 (i 1)进行碰撞反应的系统里 ,粒子增长过程中密度随时间变化规律 .本文证明了如果系数满足一定的假设 ,那么在爆炸占优的条件下 ,这一系列的平衡点在 L

The nonlinear breakage equations consist of a countable number of non-locally coupled nonlinear ordinary differentil equations modeling the concentration of the various clusters,and they describe the evolution of a system of particles undergoing coagulation and fragmentation eventsw.The interactions between clusters taken into account are restricted to the collisions of monoclusters with i-clusters,i≥1.Under fragmentation-dominated case,it is shown that the equilibria is stable in Lyapunov sense.