Determination of conductivity in a heat equation (Q5926125)

Summary: We consider the problem of determining the conductivity \(a(t)\) in the heat equation \[ u_t(x,t)= a(t) u_{xx}(x,t),\quad 0< x< 1,\quad 0< t< T \] from overspecified non-smooth boundary data. It is an ill-posed inverse problem. We apply a regularization approach to define and construct a stable approximate solution. We also perform a numerical simulation to demonstrate the accuracy of our approximation.