Solution of inverse problems in contaminant transport

Abstract: We discuss the inverse problem for contaminant transport in porous media. The nonlinear ad-sorption in equilibrium and nonequilibrium mode is included. The corresponding mathematical model of convection-diffusion-adsorption type with dominant convection is numerically approximated by time stepping and operator splitting method. An efficient numerical method is developed with small numerical dispersion to solve the direct problem and applied to the solution of ill-posed inverse problem. We focus to the determi-nation of sorption isotherms and kinetic rate of adsorption. The Lagrange method (via the adjoint system) is used to construct the gradient of the corresponding cost functional with respect to the parameters under determination. The method is applied to the dual-well setting and some numerical experiments are presented