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Some qualitative results on the dynamic viscoelasticity of the Reissner-Mindlin plate model. (English) Zbl 1079.74041
Summary: This paper is concerned with a linear viscoelastic plate model based on the Reissner-Mindlin assumption on the displacements. The initial-boundary value problems are formulated, and some qualitative results are established concerning the solutions of such problems. In fact, appropriate uniqueness and continuous data dependence results are established under various constraint restrictions upon the relaxation functions. The spatial behaviour of solutions is also studied. By assuming that the external given data have a compact support \(\widehat D_T\) on the time interval \([0,T]\), the spatial behaviour of the solution is completely described throughout the plate without the support \(\widehat D_T\).

MSC:
74K20 Plates
74D05 Linear constitutive equations for materials with memory
74H25 Uniqueness of solutions of dynamical problems in solid mechanics
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