| Contents |
| We are concerned with the dynamical behaviour of non-stationary seepage in the
flow through porous media. It is expected that the seepage of the fluid exhibits
{``\it support splitting and non-splitting phenomena"}, which are caused by the
interaction between the nonlinear diffusion and the penetration of the fluid from
the boundary on which the flowing tide and the ebbing tide occur. Here the support
means the region where the fluid exists. The model equation which describes such
phenomena is written in the form of the initial-boundary value problem for a porous
media equation. We treat it in the one-dimensional case, and demonstrate some
numerical examples which show {``\it repeated support splitting and merging phenomena"}
and {``\it non-splitting phenomena"}. From mathematical points of view we show the
stabilization theorem; that is, the solution converges to the unique stationary
solution as the time tends to the infinity. Moreover, we state some sufficient
conditions imposed on the boundary value under which such phenomena appear. |
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