一般初值下广义Becker-Döring方程的渐近性
Asymptotic behavior of the generalized Becker-Döring equations for general initial data
摘要：
对于一般的初始数据，我们证明了广义Becker-Döring系统解的以下渐近性态：在详细的平衡假设下和在密度在时间上守恒的情况下，存在临界密度$ρ_s$，使得具有初始密度$ρ_0 \leq ρ_s$的解强烈地收敛到具有密度$ρ_0$的平衡，初始密度为$ρ_0 > ρ_s$的解（在弱意义下）收敛到密度为$ρ_s$的平衡点。这扩展了以前的知识，即这种行为发生在初始数据的更严格条件下。主要的工具是一个新的估计的尾部的解决方案与密度低于临界密度。
英文摘要：
We prove the following asymptotic behavior for solutions to the generalized Becker-Döring system for general initial data: under a detailed balance assumption and in situations where density is conserved in time, there is a critical density $ρ_s$ such that solutions with an initial density $ρ_0 \leq ρ_s$ converge strongly to the equilibrium with density $ρ_0$, and solutions with initial density $ρ_0 > ρ_s$ converge (in a weak sense) to the equilibrium with density $ρ_s$. This extends the previous knowledge that this behavior happens under more restrictive conditions on the initial data. The main tool is a new estimate on the tail of solutions with density below the critical density.
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