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.
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