Local Behavior of Solutions of an Elliptic-Parabolic Equation

摘要

Consideration of the nonsteady filtration of an incompressible fluid in a homogeneous, partially saturated, porous medium leads to a degenerate nonlinear parabolic equation which is of elliptic type in the space variables in the region of degeneracy, i.e. in the saturated region. Results concerning the existence of weak solutions of such equations have been established. Here the local properties of weak solutions are studied. In particular it is shown that under the realistic assumption that the hydrostatic potential is bounded, the solution (moisture content) can be defined pointwise and is continuous. (Author).