The problem of the displacement of the interface between water and oil
of an initial form such that a cusp is formed on this interface at a
certain instant of time is considered in greater detail than in previo
us investigations. It is assumed that the viscosity of the water is ma
ny time smaller than that of the oil. Problems concerning the displace
ment of similar lines (under more general assumptions) are briefly rev
iewed. (C) 1997 Elsevier Science Ltd.