The Diffraction Problem and Verigin Problem of Quasilinear Parabolic Equation in Divergence Form for the One-dimensional Case

Abstract

In this paper, we consider the flow of two immiscible fluids in a onedimensional porous medium (the Verigin problem) and obtain a quasilinear parabolic equation in divergence form with the discontinuous coefficients. We prove first the existence and uniqueness of locally classical solution of the diffraction problem and then prove the existence of local solution of the Verigin problem.