论文标题
关于扩散的Carr-Penrose模型的全球渐近稳定性
On Global Asymptotic Stability for the diffusive Carr-Penrose Model
论文作者
论文摘要
本文与Carr和Penrose引入的线性LSW模型的扩散LSW模型的扩散扰动有关。像LSW模型一样，Carr-Penrose模型具有迅速降低自相似溶液的家族，具体取决于$ 0 <β\ le 1 $的参数$β$。结果表明，如果初始数据具有紧凑的支持，则在很大程度上对扩散模型的解决方案近似于$β= 1 $自相似的解决方案。该结果支持直觉，即扩散提供了一种机制，即LSW模型的$β= 1 $自相似解是唯一相关的解决方案。
This paper is concerned with large time behavior of the solution to a diffusive perturbation of the linear LSW model introduced by Carr and Penrose. Like the LSW model, the Carr-Penrose model has a family of rapidly decreasing self-similar solutions, depending on a parameter $β$ with $0<β\le 1$. It is shown that if the initial data has compact support then the solution to the diffusive model at large time approximates the $β=1$ self-similar solution. This result supports the intuition that diffusion provides the mechanism whereby the $β=1$ self-similar solution of the LSW model is the only physically relevant one.
