Asymptotic Profiles with Finite Mass in One-Dimensional Contaminant Transportthrough Porous Media: The Fast Reaction Case

摘要

The large time behavior of solutions of a given convection-dispersion equationwith nonlinear capacity, subject of a given initial condition, is addressed. The problem reflected in the equation and initial condition arises as a model for the one dimensional transport of a solute, with scaled concentration greater than or equal to zero, through a porous medium. In this model, the solute is assumed to undergo equilibrium adsorption with the porous matrix. An integrability condition is given which implies that initially, the total mass, both in solution and adsorbed, is finite. The physical background of the problem is discussed and the equation is derived. Some analytical properties of solutions are given. Findings are compared to referenced analytical results. The asymptotic form for pulse type solutions given a given condition is considered. The outer solutions and boundary layer solutions are discussed. The asymptotic profiles are compared with the numerical solution of the first problem. An algorithm based on a higher order Godunov approach is discussed.