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On large deflections of viscoelastic plates. (English) Zbl 1053.74560
Summary: We deal with the system of von Kármán equations describing great deflections of thin plates. Most papers mainly from the 1960s and the 1970s are devoted to stationary nonlinear systems with elliptic main parts. We concentrate on viscoelastic plates modelled by a nonstationary pseudo-parabolic system in the case of short memory and by a system with a memory term in the long memory case. The Rothe’s method converts the nonstationary problems to the sequence of stationary von Kármán equations approximating weak solutions of the original problems.

MSC:
74K20 Plates
74D10 Nonlinear constitutive equations for materials with memory
35K99 Parabolic equations and parabolic systems
35D05 Existence of generalized solutions of PDE (MSC2000)
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