Stability analysis for pattern forming systems with slowly evolving base states

While classical stability analysis usually assumes that the base state is constant in time, many patten forming systems that arise in practice have non-constant base states. We suggest an approach that applies if the evolution is slow, and that takes into account the changing instability characteristics. We present results for several problems from continuum mechanics such as Rayleigh-B\'enard convection in evaporating liquid mixtures or receding liquid and solid layers.