The mollification method and the numerical solution of the inverse heat conduction problem by finite differences (Q1123573)

The inverse heat conduction problem is mathematically improperly posed in the sense that the solution does not depend continuously upon the data. In order to cope with this difficulty, many methods have been proposed (they are mentioned in the introduction), and in the present paper, the author suggests another one. He proposes to identify the delta- mollification of the function at time t, and by this way the problem is stabilized (since the data noises are so filtered). Then he considers the discretized problem, he shows how to determine the radius of mollification as a function of the amount of noises in the data, and an illustrative example is given.