On the decay of solutions in nonsimple elastic solids with memory |
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Authors: | Vittorino Pata Ramon Quintanilla |
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Institution: | a Politecnico di Milano - Dipartimento di Matematica “F. Brioschi”, Via Bonardi 9, 20133 Milano, Italy b Matemática Aplicada 2 ETSEIAT-UPC Terrassa, Colom 11, 08222 Terrassa, Barcelona, Spain |
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Abstract: | The decay of solutions in nonsimple elasticity with memory is addressed, analyzing how the decay rate is influenced by the different dissipation mechanisms appearing in the equations. In particular, a first order dissipation is shown to guarantee the asymptotic stability of the related solution semigroup, but is not strong enough to entail exponential stability. The latter occurs for a dissipation mechanism of the second order, that is, the same order as the one of the leading operator. |
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Keywords: | Nonsimple elastic solids Dissipation of memory type Asymptotic stability Exponential stability |
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