Exponential Stability of a Certain Semigroup and Applications

D. A. Zakora

Matematičeskie zametki, Tome 103 (2018) no. 5, pp. 702-719.

Résumé

The uniform exponential stability of a $C_0$-semigroup with generator of a special form is proved. Such semigroups arise in the study of various problems of the theory of viscoelasticity. The proved statement is applied to the study of the asymptotic behavior of solutions in the problem of small motions of a viscoelastic body subject to driving forces of a special form.

Détail

Keywords: $C_0$-semigroup, integro-differential equation, exponential stability, materials with memory, asymptotics.

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