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Mathematics and Mechanics of Solids
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Some Results in the Dynamics of Viscoelastic Mixtures

C. Gales

Faculty of Mathematics, University of Iasi, 700506-Iasi, Romania

The present article studies some qualitative properties of solutions in the dynamics of viscoelastic mixtures made by two constituents: a porous elastic solid and a viscous fluid. In this sense, some results concerning the theory of semigroups of linear operators are used to establish the existence and uniqueness of the weak solutions of the initial boundary value problems associated with the linear theory. The continuous dependence problem upon initial data and supply terms is also investigated. Then, the temporal behavior is studied in terms of the Cesáro means of various parts of the total energy. The relations that describe the asymptotic behavior of mean energies are established by using some Lagrange—Brun identities.

Key Words: Viscoelastic mixture • existence and uniqueness of weak solutions • asymptotic partition of energy

This version was published on April 1, 2008

Mathematics and Mechanics of Solids, Vol. 13, No. 2, 124-147 (2008)
DOI: 10.1177/1081286506075030
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