A model, called pressure-driven growth, is analysed for propagation of a foam front through an oil reservoir during improved oil recovery using foam. Numerical simulations of the model predict, not only the distance over which the foam front propagates, but also the instantaneous front shape. A particular case is studied here in which the pressure used to drive the foam along is suddenly increased at a certain point in time. This transiently produces a concave front shape (seen from the domain ahead of the front): such concavities are known to be delicate to handle numerically. As time proceeds however, the front evolves back towards a convex shape, and this can be predicted by a long-time asymptotic analysis of the model. The increase in driving pressure is shown to be beneficial to the improved oil recovery process, because it gives a more uniform sweep of the oil reservoir by the foam.