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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.

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