Nonlinear convection-dispersion models with a distributed pollutant source I: Direct initial boundary value problems

This paper deals with the modeling and solution of a class of nonlinear direct problems related to a transport diffusion model with a source term. Specifically, the first part of the paper deals with the derivation of a class of transport and diffusion models (with a distributed source term) in one space dimensions with variable properties along the channel and nonlinear decay term. The second part with simulations, that is the approximation to the solution of nonlinear initial boundary value problems by generalized collocation methods. The third part develops a critical analysis mainly addressed to research perspectives on the solution of inverse problems related to the identification of the source term.