Identification of the population density of a species model with nonlocal diffusion and nonlinear reaction. (5th April 2017)

• Record Type: Journal Article
• Authors: Tuan, Nguyen Huy; Au, Vo Van; Khoa, Vo Anh; Lesnic, Daniel
• Is Part Of: Inverse problems. Volume 33:Number 5(2017:May)
• Publication Date: 2017-04-05
• Subjects: inverse problem -- nonlocal diffusion -- nonlinear reaction -- ill-posed problem -- population density; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/aa635f
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: The identification of the population density of a logistic equation backwards in time associated with nonlocal diffusion and nonlinear reaction, motivated by biology and ecology fields, is investigated. The diffusion depends on an integral average of the population density whilst the reaction term is a global or local Lipschitz function of the population density. After discussing the ill-posedness of the problem, we apply the quasi-reversibility method to construct stable approximation problems. It is shown that the regularized solutions stemming from such method not only depend continuously on the final data, but also strongly converge to the exact solution in L 2 -norm. New error estimates together with stability results are obtained. Furthermore, numerical examples are provided to illustrate the theoretical results.