A PDE model and its solution about the stratum hurting in the water injection well

A new model of describing the stratum hurting in the water injection well is established by using two dimensional parabolic partial different equations,and then,its initial and boundary value problems with discontinuity coefficient are obtained by simplifying.Based on the convergence of the solution of the difference equations,we construct difference scheme by applying integration-relation method.Finally,some applications of the model are given.