A method for the approximate solution of an inverse problem for the heat- conduction equation (Q1803481)

An inverse problem for the one-dimensional heat equation is investigated. The boundary condition at one edge is sought for under the assumption that the solution at the second edge is given with a definite accuracy. An approximate solution to the problem is proposed by means of a transformation of the heat equation into a hyperbolic equation with a small parameter at a second derivative. The proof of convergence of the approximate solutions to the accurate one is presented.