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Existence and dissipativity for the one-dimensional dynamic problem of the linear viscoelasticity. (Italian. English summary) Zbl 0715.73028
Summary: We consider the one-dimensional dynamic problem for a linear viscoelastic material in the Sobolev space $$H^{1,2}$$. We prove the existence of the solution, for a suitable class of data and for convex relaxation function which has the equilibrium modulum strictly positive.

##### MSC:
 74D05 Linear constitutive equations for materials with memory 74D10 Nonlinear constitutive equations for materials with memory 74Hxx Dynamical problems in solid mechanics 45K05 Integro-partial differential equations 46F10 Operations with distributions and generalized functions