Displacement of oil by water in a single elastic capillary

Abstract In this paper we consider the evolution of a free boundary separating two immiscible viscous fluids with different constant densities. The joint motion of liquids in the solid skeleton is described by Stokes equations coupled with Lamé equations, driven by the input pressure and the force of gravity. We prove the existence and uniqueness of classical solutions global in time, and we emphasize the study of the properties of the moving boundary separating the two fluids

The Stefan problem

The Stefan Problem (Kirchen Der Welt

Palmer LTER: Impact of a Large Diatom Bloom on Macronutrient Distribution in Arthur Harbor During Austral Summer 1991-1992

We present here an improved version of the method introduced by the first author to derive pointwise gradient estimates for the solutions of one-dimensional parabolic problems. After considering a general qualinear equation in divergence form we apply the method to the case of a nonlinear diffusion-convection equation. The conclusions are stated first for classical solutions and then for generalized and mild solutions. In the case of unbounded initial datum we obtain several regularizing effects for t > 0. Some unilateral pointwise gradient estimates are also obtained. The case of the Dirichlet problem is also considered. Finally, we collect, in the last section, several comments showing the connections among these estimates and the study of the free boundaries associated to the solutions of the diffusion-convection equation