An inverse problem for the identification of an unknown spatially dependent coefficient in a parabolic partial differential equation is considered as an application for this new technique. An integral identity which explicitly relates changes in coefficients to changes in measured data is presented. Using this identity, it is possible to show that the coefficient to data map is continuous, strictly monotone and injective. Applying a modified Backus-Gilbert method to this identity generates a sequence of coefficients converging to the required unknown coefficient. Finally, implementation of the procedure is discussed and some numerical experiments are displayed.
"Identification of Some Spatially Variable Physical Properties." Missouri J. Math. Sci. 20 (2) 138 - 149, May 2008. https://doi.org/10.35834/mjms/1316032814