Correctness of the free boundary problem for the microscopic in-situ leaching model

We consider initial boundary value problem for in-situ leaching process of rare metals at the microscopic level. this physical process describes by the stokes equations for the liquid component coupled with the lame's equations for the solid skeleton and the diffusion-convection equations for acid concentration. due to the dissolution of the solid skeleton, the pore space has an unknown (free) boundary. for formulated initial boundary-value problem we prove existence and uniqueness of the classical solution