Mathematical Problems in the Theory of Bone Poroelasticity
Keywords:poroelasticity, double porosity, boundary value problems.
AbstractThis paper concerns with the quasi-static theory of bone poroelasticity for materials with double porosity. The system of equations of this theory based on the equilibrium equations, conservation of fluid mass, the effective stress concept and DarcyвЂ™s law for material with double porosity. The internal and external basic boundary value problems (BVPs) are formulated and uniqueness of regular (classical) solutions are proved. The single-layer and double-layer potentials are constructed and their basic properties are established. Finally, the existence theorems for classical solutions of the BVPs are proved by means of the potential method (boundary integral method) and the theory of singular integral equations.
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