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A polynomial way to control the decay of solutions for dipolar bodies. (English) Zbl 1442.74013

Summary: In our paper, we consider a combination of two sub-cylinders coupled by an interface in a semi-infinite cylinder. Both sub-cylinders are made of dipolar elastic materials. For one of the two sub-cylinders, we will consider the elastostatic problem, and for the other the elastodynamic problem. Thus, the spatial behaviors of the sub-cylinders are of different kind and the question arises whether the evolution of this combination can be controlled. By using a polynomial way, we prove that the decay of solutions for the two problems can be controlled.

MSC:

74A35 Polar materials
74B10 Linear elasticity with initial stresses
74G10 Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of equilibrium problems in solid mechanics
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