Regularization of the backward-in-time Kuramoto–Sivashinsky equation

We are interested in solution techniques for backward-in-time evolutionary PDE problems arising in fluid mechanics. In addition to their intrinsic interest, such techniques have applications in the recently proposed retrograde data assimilation. As our model system we consider the terminal value problem for the Kuramoto–Sivashinsky equation in a 1D periodic domain. Such backward problems are typical examples of ill-posed problems, where any …