两群人口方程的适定性与谱特征

Well-posedness and Spectral Characteristics of a Two-group Population Equation

建立了两群人口发展的数学模型,讨论了相应两群人口算子的谱分布,证明了两群人口算子的谱由至多可数个孤立的有限重的本征值构成,运用有界线性算子半群理论,证明了两群人口方程解的存在唯一性.

A two-group population model was formulated.The spectral distribution of corresponding population operator was discussed.It was showed that the spectrum set of this operator consisted of countable isolated eigenvalues at most with finite multiplicity.By applying semigroup theory of bounded linear operators,the existence and uniqueness of the solution of the corresponding population system were proved.