非光滑边界条件下具时滞的Rotenberg方程主算子的谱分析

Abstract

Abstract:

After considering the time delay of cell division, the Rotenberg transport equation with time-delay is introduced in this paper. In $L_1$ space, under the condition of non-smooth boundary (the boundary operator is unbounded), it is proved that the transport operator can generate a $C_0$-semigroup. Furthermore, we study the spectrum of the transport operator and prove that the region $\Gamma=\sigma(A_H)\cap \{\lambda\in C | {\rm Re}\lambda>\gamma\}$ ($\gamma>{\rm max}\{\lambda_0, -\sigma_0\}$) is only consists of a finite number of discrete eigenvalues with finite algebraic multiplicity.

Key words: Rotenberg equation, Transport operators, Nonsmooth boundary conditions, Spectrum analysis, Time delay

CLC Number:

O177.2

Yage Tong,Kaisu Wu. Spectral Analysis of the Main Operator of Rotenberg Equation with Time Delay Under Nonsmooth Boundary Conditions[J].Acta mathematica scientia,Series A, 2022, 42(5): 1320-1331.

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References 18

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Spectral Analysis of the Main Operator of Rotenberg Equation with Time Delay Under Nonsmooth Boundary Conditions

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