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The paper presents the proofs of two theorems of uniqueness of the solution of the mixed boundary-initial value problem for elastic Cosserat continuum. The first of the theorems deals with an anisotropic material and is deduced for bounded regions. Except for certain symmetry no restrictive assumptions are imposed on the anisotropy tensors. The second theorem concerns an isotropic material and is formulated for a certain class of unbounded regions. In addition to the inequalities that are necessary and sufficient for positive definitness of the strain energy density, two other restrictive inequalities must be assumed for the material constants.
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