london-journal-of-humanities-and-social-science London Journal of Humanities and Social Science 2515-5784 2515-5792 JournalsPress 64785 A Inverse Problem of Determination of Coefficient in Parabolic Equations as a Generalized Moments Problem 19 5

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

 Full Text

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.