Abstract
We consider the problem of finding a pair of functions b(t) and w(x, t) that satisfy the equation b(t)wt(x, t) = wxx(x, t) + r(x, t), 0 < x < 1 , t > 0, under the initial condition w(x, 0) = ??(x), 0 ?? x ?? 1 , and boundary conditions w(0, t) = 0; wx(0, t) = wx(1, t), t ? 0, plus R 1 0 w(x, t)dx = E(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.
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