The problem of the nonlinear diffusive predator–prey model with the same biotic resource. (April 2017)

• Record Type: Journal Article
• Authors: Jau, Guo-Chin
• Is Part Of: Nonlinear analysis. Volume 34(2017)
• Page Start: 188
• Page End: 200
• Publication Date: 2017-04
• Subjects: Diffusive predator–prey model -- Biotic resource -- Upper–lower solution -- Semigroup; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2016.08.011
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: In recent years, the research on the diffusive predator–prey model has attracted much attention. In these models, the carrying capacity is considered as a constant. In 2013, H. M. Safuan investigated the system of a predator and prey that shares the same biotic resource, where the carrying capacity is a function of the time. The spatial component of ecological interactions has been recognized as an important factor. So, we will discuss the problem of the nonlinear diffusive predator–prey model with the same biotic resource. This model is the system of the nonlinear partial differential equations with zero-flux boundary condition. The main objective of the present paper is to investigate the existence and uniqueness of the solution of this model. In this paper, we also obtain that there is a unique solution of the nonlinear partial differential equations with Dirichlet boundary condition.