Recovering the Initial Condition of Parabolic Equations from Lateral Cauchy Data As a Generalized Problem of Moments

It will be shown that to recover the initial condition and finding the solution of a parabolic equation with Cauchy conditions can be solved in two steps writing the parabolic equation as an integral equation, which can be solved numerically applying the techniques of inverse generalized moments problem. In a first step, the initial condition is found in approximate form, and in a second step we numerically approximate the solution of the parabolic equation using the initial condition found. The method is illustrated with examples.