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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
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