A convection-diffusion problem in a network

In recent years, it has become increasingly dear that the standard method of modeling hydrodynamic dispersion in groundwater flow by diffusion is often unsatisfactory. In the last few years, several authors have tried to overcome this problem by modeling subsurface flow by flow in a network. This has had some success and even some agreement with experiment. This work will lay the mathematical foundations for such models which, up to this point in time, have been studied only numerically. A well-posedness result is obtained for a class of these models. Some qualitative properties of solutions, such as positivity, ordering, and boundedness are also given. (C) 2000 Elsevier Science Inc. All rights reserved.