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Abstract Recent observations of increased discharge through fast-flowing outlet glaciers and ice streams motivate questions concerning the inland migration of regions of fast flow, which could increase drawdown of the ice-sheet interior. To investigate one process that could lead to inland migration we conduct experiments with a two-dimensional, full-stress, transient ice-flow model. An initial steady state is perturbed by initiating a jump in sliding speed over a fraction of the model domain. As a result, longitudinal-stress gradients increase frictional melting upstream from the slow-to-fast sliding transition, and a positive feedback between longitudinal-stress gradients, basal meltwater production and basal sliding causes the sliding transition to migrate upstream over time. The distance and speed of migration depend on the magnitude of the perturbation and on the degree of non-linearity assumed in the link between basal stress and basal sliding: larger perturbations and/or higher degrees of non-linearity lead to farther and faster upstream migration. Migration of the sliding transition causes the ice sheet to thin over time and this change in geometry limits the effects of the positive feedback, ultimately serving to impede continued upstream migration.