A Inverse Problem of Determination of Coefficient in Parabolic Equations as a Generalized Moments Problem

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 ƒ?? x ƒ?? 1 , and boundary conditions w(0, t) = 0; wx(0, t) = wx(1, t), t ƒ? 0, plus R 1 0 w(x, t)dx = E(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.

The authors declare no conflict of interest.

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The datasets used in this study are openly available at [repository link] and the source code is available on GitHub at [GitHub link].

This work did not receive any external funding.