An Inverse Problem for the Steady State Diffusion Equation
Gerard R. Richter · SIAM Journal on Applied Mathematics · 1981
We consider the problem of identifying a spatially varying diffusion coefficient using an observed solution to the forward problem. Under appropriate conditions, this problem can be treated as a first order hyperbolic equation in the unknown coefficient. We develop some continuous dependence results for this problem, and also propose a particularly advantageous set of test conditions for observing the forward solution.