208	1998	Jonas Nilsson	jonasn@tdb.uu.se	An Inverse Problem for Diffusion Chemical Processes

Abstract

An inverse problem for two diffusion chemical processes is
studied. The inverse problem is solved by computing the solution to
the direct problem and compare the solution with known experimental
data in an iteratively procedure, leading to the determination of the
unknown physical parameters. The difference between known data and
computed data have been formulated as a least square sum, and
minimized with respect to the unknowns.

The first problem is a plain diffusion equation with a time dependent
boundary condition, for which we derive the analytical solution to the
direct problem. With a conditioning analysis we show that this inverse
problem is well-posed for feasible values of the physical parameters.

For the second problem, i.~e. a diffusion equation coupled to a
first-order reversible chemical reaction, we show that the direct
problem is well-posed. To solve this direct problem we use finite
difference approximations on overlapping grids, which is a general
methodology that gives fast and accurate results.

We achieve good results with our technique when solving the inverse
problem for these two diffusion chemical processes. The computed
values on the unknowns give an almost perfect fit to the experimental
data. Therefore, we conclude that our technique is a robust and an
accurate method for solving the inverse problem.