A note on an ill-posed problem for the heat equation
Giorgio Talenti, Sergio Vessella · Journal of the Australian Mathematical Society Series A Pure Mathematics and Statistics · 1982
Abstract In this paper an ill-posed problem for the heat equation is investigated. Solutions u to the equation ut – uxx = 0, which are approximately known on the positive half-axis t = 0 and on some vertical lines x = x1,…, x = xn, are considered and stability estimates of these solutions are presented. We assume an a priori bound, governing the heat flow across the boundary x = 0.