ftp ejde.math.txstate.edu (login: ftp) A NONHOMOGENEOUS BACKWARD HEAT PROBLEM: REGULARIZATION AND ERROR ESTIMATES

Abstract. We consider the problem of finding the initial temperature, from the final temperature, in the nonhomogeneous heat equation ut − uxx = f(x, t), (x, t) ∈ (0, pi) × (0, T), u(0, t) = u(pi, t) = 0, (x, t) ∈ (0, pi) × (0, T). This problem is known as the backward heat problem and is severely ill-posed. Our goal is to present a simple and convenient regularization method, and sharp error estimates for its approximate solutions. We illustrate our results with a numerical example. 1