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Uniqueness and dissipativity for the one-dimensional dynamic problem of the linear viscoelasticity. (Italian. English summary) Zbl 0715.73027
Summary: We consider the one-dimensional dynamic problem for a linear viscolastic material in the Sobolev space $$H^{1,2}$$. We prove the uniqueness of the solution for the class of convex relaxation functions. Moreover we prove that this uniqueness is strictly related to the prefixed Sobolev space.

##### MSC:
 74D05 Linear constitutive equations for materials with memory 74D10 Nonlinear constitutive equations for materials with memory 74Hxx Dynamical problems in solid mechanics 74G30 Uniqueness of solutions of equilibrium problems in solid mechanics 74H25 Uniqueness of solutions of dynamical problems in solid mechanics 45K05 Integro-partial differential equations 46F10 Operations with distributions and generalized functions
##### Keywords:
Sobolev space; convex relaxation functions