## Abstract

We study a class of second order hyperbolic systems with dissipation which describes viscoelastic materials. The considered dissipation is given by the sum of the memory term and the damping term. When the dissipation is effective over the whole system, we show that the solution decays in L^{2} at the rate t^{- n / 4} as t → ∞, provided that the corresponding initial data are in L^{2} ∩ L^{1}, where n is the space dimension. The proof is based on the energy method in the Fourier space. Also, we discuss similar systems with weaker dissipation by introducing the operator (1 - Δ)^{- θ / 2} with θ > 0 in front of the dissipation terms and observe that the decay structure of these systems is of the regularity-loss type.

Original language | English |
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Pages (from-to) | 621-635 |

Number of pages | 15 |

Journal | Journal of Mathematical Analysis and Applications |

Volume | 366 |

Issue number | 2 |

DOIs | |

Publication status | Published - Jun 15 2010 |

## All Science Journal Classification (ASJC) codes

- Analysis
- Applied Mathematics