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

London Journal of Research in Science: Natural and Formal
Volume | Issue | Compilation
Authored by María Beatriz Pintarelli , NA
Classification: For code: 010599
Keywords: generalized moment problem, solution stability, integral equations, parabolic equation, coefficient determination.
Language: English

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) = φ(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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