A globally convergent numerical method for a coefficient inverse problem for a parabolic equation

摘要

In this work a Multidimensional Coefficient Inverse Problem (MCIP) for a parabolic PDE with the data resulting from a single measurement event is considered. This measured data is obtained using a single position of the point source. The most important property of the method presented here is that even though we do not need any advanced knowledge of a small neighborhood of the solution, we still obtain points in this neighborhood. This is the reason why the numerical algorithm for this method is called globally convergent. In the literature a globally convergent numerical method for the MCIP with single measurement data has inclusively been considered in the book (Beilina and Klibanov, 2012) and some other publications of Beilina and Klibanov. In those publications a globally convergent algorithm for MCIP for a hyperbolic PDE was developed. Here we modify their technique to prove the global convergence property of their method for the parabolic case.