A GENERAL NONLINEAR MODEL FOR THE INTERACTION OF A SIZE-STRUCTURED POPULATION AND ITS ENVIRONMENT: WELL-POSEDNESS AND APPROXIMATION

作者：Ackleh Azmy S^*; Ma Baoling; Miller Robert

来源：Quarterly of Applied Mathematics, 2016, 74(4): 671-704.

DOI：10.1090/qam/1439

• Structured population model
• environment
• finite difference approximations
• convergence
• well-posedness

We present a general model for the interaction of a size-structured population with its environment. The vital rates of the individuals are assumed to depend on a number of variables including the total population and the environment. We develop a finite difference approximation for this general model and prove the convergence of the method to the unique weak solution of the nonlinear system of partial differential equations coupled with ordinary differential equations. Potential applications are presented in various fields ranging from blood cell population dynamics to the study of invasive species.

• 出版日期2016