Dynamical analysis of a model of harmful algae in flowing habitats with variable rates. (April 2015)

• Record Type: Journal Article
• Authors: Abbas, Syed
• Is Part Of: Nonlinear analysis. Volume 22(2015)
• Page Start: 16
• Page End: 33
• Publication Date: 2015-04
• Subjects: Advection dispersion equation -- Analytic semigroup -- Spectral bound -- Rothe method; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2014.06.001
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: This study considers an advection–dispersion–reaction model of harmful algae in a flowing water habitat. The habitat is selected such that the main channel is coupled with a storage zone. The rates are considered to be time dependent instead of constant, which is more natural. The introduction of variable rates makes the system difficult to study. We prove the well-posedness and boundedness using the evolution semigroup approach. Often, it is difficult to find an analytical solution for a given model, thus approximate solutions are very useful and it is important to study them. In the second part, we use a discretization method to find the approximate solution of our model system.