On a nonlinear system consisting of three different types of differential equations (Q532070)

The paper under review deals with a system of differential equations consisting of a first order ODE, a parabolic and an elliptic PDE of general divergence form. The equations may contain nonlocal terms by which the author means mostly some (time or space) integral of the unknowns. As a motivation for this problem a fluid flow model in porous medium is shown. The author proves existence of weak solutions by applying the Schauder fixed point theorem. The assumptions are generalizations of the classical conditions of Lions, some ideas from the theory of monotone operators are also used. The results are illustrated with examples.