Physical Sciences and Mathematics Commons^™

Parameter Estimation In Nonlinear Coupled Advection-Diffusion Equation, Robert R. Ferdinand

Applications and Applied Mathematics: An International Journal (AAM)

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.