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**Some energetic properties of smooth solutions in rate-type viscoelasticity.**
*(English)*
Zbl 0553.73026

Some energetic properties of the smooth solutions of initial and boundary value problems in the semilinear rate-type theory of viscoelasticity are pointed out. The existence of a unique convex energy function having certain monotony properties with respect to the equilibrium curve is proved. For an isolated body the asymptotic approach to equilibrium (in the \(L_ 2\) sense) is shown. This property is used to obtain a rate-type viscoelasticity approach of nonlinear elasticity. Sufficient stability conditions are given for the solutions of the one-dimensional problem and for the three-dimensional problem with small strains.

Reviewer: Gh.Gr.Ciobanu

### MSC:

74Hxx | Dynamical problems in solid mechanics |

74A20 | Theory of constitutive functions in solid mechanics |

74B20 | Nonlinear elasticity |

74S30 | Other numerical methods in solid mechanics (MSC2010) |