非光滑边界条件下具时滞的Rotenberg方程主算子的谱分析

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

该文考虑细胞分裂的时滞性,引入了具时滞的Rotenberg迁移方程,在L1空间中非光滑边界条件下(边界算子无界),证明迁移算子生成C_(0)-半群,并进一步分析迁移算子的谱,得到该迁移算子的谱在区域Γ=σ(AH)∩{λ∈C|Reλ>γ}(γ>max{λ_(0),−σ_(0)})中仅由有限个具有有限代数重数的离散本征值组成等结果(λ_(0),−σ_(0)的具体意义见正文).

After considering the time delay of cell division,the Rotenberg transport equation with time-delay is introduced in this paper.In L1 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 regionΓ=σ(AH)∩{λ∈C|Reλ>γ}(γ>max{λ_(0),−σ_(0)})is only consists of a finite number of discrete eigenvalues with finite algebraic multiplicity.