A Nonlinear Problem Related to Artificial Circulation in a Lake

Abstract

This work deals with artificial circulation as a shallow water aeration technique. Large waterbodies (for instance, lakes or reservoirs) get much of their oxygen from the atmosphere through diffusion processes. Artificial circulation increases water’s oxygen by forcefully circulating the water to expose more of it to the atmosphere. Two techniques are the most common: air injection and mechanical mixing. The former has been analyzed from an ecological viewpoint in several works (see, for instance Haynes in Hydrobiologia 43:463–504, 1973 [1] and the references therein). However, in this work we will focus our attention on the latter that, as far as we know, has remained unaddressed in the mathematical literature. In this work we introduce the mathematical formulation of the environmental problem as a system of nonlinear partial differential equations more general than that studied by Martínez et al. (Math. Control Relat. Fields 8:277–313, 2018 [2]), and we prove the existence of solution using a fixed point technique. This work was supported by funding from project MTM2015-65570-P of Ministerio de Economía y Competitividad (Spain)/FEDER.