A semi-implicit monotone difference scheme for an initial-boundary value problem of a strongly degenerate parabolic equation modeling sedimentation-consolidation processes

摘要

We prove the convergence of a semi-implicit monotone finite difference scheme approximating an initial-boundary value problem for a spatially one-dimensional quasilinear strongly degenerate parabolic equation, which is supplied with two different inhomogeneous flux-type boundary conditions. This problem arises in the modeling of the sedimentation-consolidation process. We formulate the definition of entropy solution of the model in the sense of Kruzkov and prove convergence of the scheme to the unique BV entropy solution of the problem, up to satisfaction of one of the boundary conditions.