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Milan Journal of Mathematics

, 77:333 | Cite as

Stability and exponential stability in linear viscoelasticity

  • Vittorino PataEmail author
Article

Abstract

In this survey paper, we discuss the decay properties of the semigroup generated by a linear integro-differential equation in a Hilbert space, which is an abstract version of the equation
$${\partial_{tt}}u(t) - \Delta u(t) + {\int_0^\infty} \mu(s) \Delta u(t - s) {\rm{d}}s = 0$$
describing the dynamics of linearly viscoelastic bodies.

Mathematics Subject Classification (2000)

35B40 45K05 45M10 47D06 

Keywords

Linear viscoelasticity memory kernels contraction semigroups stability exponential stability 

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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2009

Authors and Affiliations

  1. 1.Politecnico di Milano - Dipartimento di Matematica “F.Brioschi”MilanoItaly

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