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On weak solutions to a viscoelasticity model. (English) Zbl 0719.73014
This paper is concerned with a dynamic theory of viscoelastic materials of integral type. The authors consider a constitutive law where the memory response is linear and the kernel has certain special properties. The existence of global in time weak solutions is proved. First, the authors use the Galerkin method to construct approximate solutions. Then, the method of monotone operators is used to solve the convergence.
Reviewer: D.Ieşan (Iaşi)

MSC:
74D99 Materials of strain-rate type and history type, other materials with memory (including elastic materials with viscous damping, various viscoelastic materials)
45K05 Integro-partial differential equations
74D05 Linear constitutive equations for materials with memory
74D10 Nonlinear constitutive equations for materials with memory
49M15 Newton-type methods
49J52 Nonsmooth analysis
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