摘要
研究一个带有时滞的血红细胞模型的解展开问题.对模型在平衡点处线性化,并利用泛函分析方法,将线性化模型写成抽象发展方程.借助半群理论证明了方程的适定性.对系统算子细致的谱分析,得到了本征值的渐近表达式.通过对算子的Riesz谱投影范数的渐近估计,证明系统的本征向量不能构成状态空间的基,但我们仍给出了方程的解在平衡点附近按照本征向量的的渐近展开.
In this paper, the expansion of the solution of a red blood cells model with one delay is considered. First, the model near its equilibrium is linearized and the linearized model is rewritten as abstract evolutionary equation. Then, the well-posed-ness of the equation is obtained by applying the theory of Co semigroup. With a detailed spectral analysis, the explicit asymptotical expressions of all eigenvalues are given. Finally, it is shown that the eigenvectors of the system fail to form a basis for the Hilbert state space by estimating the norm of Riesz projection of the system operator. However, the asymptotic expansion of the solution associated with the eigenvectors is given.
出处
《系统科学与数学》
CSCD
北大核心
2009年第8期1009-1027,共19页
Journal of Systems Science and Mathematical Sciences
基金
国家自然科学基金(NSFC-60874034)资助项目
关键词
血红细胞
时滞
C0半群
解的渐近展开
Red blood cell, delay, Co semigroup, asymptotic expansion of solution