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 ?? x ?? 1 , and boundary conditions wx(0, t) = s(t) ; wx(1, t) = l(t), t ? 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.
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 ?? x ?? 1 , and boundary conditions wx(0, t) = s(t) ; wx(1, t) = l(t), t ? 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.