Stability Analysis For Size-structured Population Models With Delayed Birth Process

In this dissertation, we mainly carry out the analysis of well-posedness and stability of solutions for size-structured systems with delayed birth process. We consider separately two cases:the general case and the case that the systems depend on age and resource.We first transfer the models into Cauchy problems of abstract evolution equations, and we prove the existence, uniqueness and well-posedness of solutions by using the theory of strongly continuous semigroup. Then, through the analysis of resolvent operators and compact semigroup, we investigate the regularity for the generated semigroup, and abtain the characteristic equations. We establish successfully the conditions of stability and instability for stationary solutions of the population systems.Based on the existed work in literatures on the size-structured population models, we further consider in this dissertation the effects of delays in the birth process and resources on the asymptotic behaviors of the solutions. The theory and the techniques of delayed semigroup are applied here to discuss the problems. Our obtained results develop and extend the corresponding existed conclusions.