A river water quality model for time varying BOD discharge concentration (Q1960785)

The authors consider a model for biochemical oxygen demand (BOD) described by a partial differential equation. The BOD is prescribed by a time varying function at the left endpoint. This implies to study the problem with a time varying boundary loading. The well-posedness is obtained for the model when the boundary loading is smooth in time. Qualitative results such as ordering, positivity and boundedness are also obtained. The main result consists in proving that a periodic loading function admits a unique asymptotically attracting periodic solution. For non-smooth loading functions, only weak solutions are obtained. In a special case the paper proves the existence of explicit solutions in the form of infinite series (Fourier series). Numerical experiments are given.