Inverse Source Identification on Poisson Equation with Cauchy Conditions As a Generalized Problem of Moments

Abstract

We consider the problem of finding a pair of functions φ( x, t) and w( x, t) that satisfy the equation wxx( x, t) + wtt( x, t) = φ( x, t) under Cauchy boundary conditions. We will see that an approximate solution can be found using the techniques of generalized inverse problem of moments and find dimensions for the error of the estimated solution.