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On dynamics of viscoelastic multidimensional medium with variable boundary. (English) Zbl 1034.35141

This paper is about a theorem of uniqueness and existence, local in time, for the solution of an initial boundary value problem of a system of equations that the author say to be of interest in the modelling of viscoelastic materials. The theorem is established in classes of summable functions under suitable conditions on the data and variable boundaries. The mechanical issues of the problem are not clearly presented and informations on this side are not easy to be obtained also by using the references. The author claims that the model is of interest for a viscous continuous medium with a memory along the particles. It is not clear if the elastic part of the model is frame-indifferent (see the generalization proposed after the introduction of the isotropic representation formula (1.7)) where the left Cauchy-Green tensor instead of the right one is used.

MSC:

35Q72 Other PDE from mechanics (MSC2000)
35Q99 Partial differential equations of mathematical physics and other areas of application
74B20 Nonlinear elasticity
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