Solving the Heat Source Inverse Problem with Moments Problems Tecniques

Abstract

We consider the problem of finding a pair of functions ??(x, t) and w(x, t) that sat- isfy the equation wt(x, t) = wxx(x, t) + ??(x, t), 0 < x < 1 , t > 0, under the ini- tial condition w(x, 0) = w0(x), 0 ƒ?? x ƒ?? 1 , and boundary conditions wx(0, t) = s(t) ; wx(1, t) = l(t), t ƒ? 0. 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.