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

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 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.

Keywords

coefficient determination. generalized moment problem integral equations parabolic equation solution stability

  • Research Identity (RIN)

  • License

    Attribution 2.0 Generic (CC BY 2.0)

  • Language & Pages

    English, Array-Array

  • Classification

    For code: 010599