Determination of space-time-dependent source terms in the integer-fractional mobile-immobile solute transport system

Abstract

We consider a numerical inversion problem of determining two space-time-dependent source terms in the integer-fractional mobile-immobile solute transport model by using the Dirichlet-Neumann boundary data. The unique existence of a solution to the forward problem is obtained by the inverse Laplace transform, and a dynamical system connecting the known data with the unknown sources is established by the variational method and boundary homogenization. The dynamical system is discretized to a linear system at given time in the homogenized polynomial space, and the source functions can be reconstructed by the alternative iteration and Tikhonov regularization. Two examples are presented to illustrate the validness of the inversion algorithm. MSC(2010) 35R11; 35R30; 65N21