Abstract
A new class of unilaterally constrained problems for fully coupled poroelastic models stemming from hydraulic fracturing is introduced and studied with respect to its well-posedness. The poroelastic medium contains a fluid-driven crack, which is subjected to non-penetration conditions and cohesion forces between the crack faces. Existence of solution for the governing elliptic–parabolic variational inequality under the unilateral constraint with a small cohesion is established using the incremental approximation based on Rothe’s semi-discretization in time.
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