On Inverse Source Problems for Groundwater Modeling

Abstract

In this paper, we consider a number of inverse source problems for modeling Groundwater water flow. We start with a general model in which storativity and conductivity are taken to be time and space dependent. Different forms of storativity and conductivity are then considered. Solutions to these problems are presented in the form of series expansions of orthogonal bases obtained by solving the corresponding homogeneous problems using separation of variables. The obtained series solutions include Fourier sine, Fourier-Bessel and Fourier-Legendre series. In the discussed problems, the source term is taken to be space dependent only or space and time dependent, where the space dependent part is given.

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