A TOXIN-MEDIATED SIZE-STRUCTURED POPULATION MODEL: FINITE DIFFERENCE APPROXIMATION AND WELL-POSEDNESS

作     者：Huang, Qihua Wang, Hao 

作者机构：Univ Alberta Dept Math & Stat Sci Edmonton AB T6G 2G1 Canada 

出 版 物：《MATHEMATICAL BIOSCIENCES AND ENGINEERING》 (Math. Biosci. Eng.)

年 卷 期：2016年第13卷第4期

页      面：697-722页

核心收录：

学科分类：0710[理学-生物学] 07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：Alberta Environment and Sustainable Resource Development Alberta Water Research Institute NSERC 

主　　题：Size-structured model toxin finite difference approximation existence-uniqueness 

摘      要：The question of the effects of environmental toxins on ecological communities is of great interest from both environmental and conservational points of view. Mathematical models have been applied increasingly to predict the effects of toxins on a variety of ecological processes. Motivated by the fact that individuals with different sizes may have different sensitivities to toxins, we develop a toxin-mediated size-structured model which is given by a system of first order fully nonlinear partial differential equations (PDEs). It is very possible that this work represents the first derivation of a PDE model in the area of ecotoxicology. To solve the model, an explicit finite difference approximation to this PDE system is developed. Existence-uniqueness of the weak solution to the model is established and convergence of the finite difference approximation to this unique solution is proved. Numerical examples are provided by numerically solving the PDE model using the finite difference scheme.