In this paper a coupled system of two nonlinear advection-diffusion equations is presented. Such systems of equations have been used in mathematical literature to describe the dynamics of contaminant present in groundwater flowing through cracks in a porous rock matrix and getting absorbed into it. An inverse method procedure that approximates infinite-dimensional model parameters is described and convergence results for the parameter approximants are proved. This is finally followed by a computational experiment to compare theoretical and numerical results to verify accuracy of the mathematics analysis presented.
Ferdinand, Robert R.
Parameter Estimation in Nonlinear Coupled Advection-Diffusion Equation,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 2,
1, Article 1.
Available at: https://digitalcommons.pvamu.edu/aam/vol2/iss1/1