血红细胞时滞模型的谱及其解的结构

SPECTRAL ANALYSIS AND SOLUTION STRUCTURE OF A RED BLOOD CELLS MODEL WITH ONE DELAY

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.