## Abstract.

The purpose of this paper is to consider a two-dimensional version of the Aifantis equation of statics of the theory of consolidation with double porosity and effectively solve the basic BVPs for the half-plane. We extend the potential method and the theory of integral equations to BVPs of the theory of consolidation with double porosity. For all problems, we construct Fredholm type integral equations. For the Aifantis equation of statics we construct a particular solution and reduce the solution of the basic BVPs of the theory of consolidation with double porosity to the solution of the basic BVPs for the equation for an isotropic body. A Poisson type formula is constructed for the solution of the first and of the second boundary value problem for the half-plane.

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