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General Decay of Solutions of a Weak Viscoelastic Equation

  • Research Article - Mathematics
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Abstract

In this paper we consider the following viscoelastic equation

$$ u_{tt}-\Delta u +\alpha (t)\int_{0}^{t} g (t-\tau )\Delta u(\tau) \,{\rm d} \tau =0, $$

in a bounded domain, and establish a general decay result which depends on the behavior of α and g. This work generalizes and improves earlier results in the literature.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran, 31261, Saudi Arabia

    Salim A. Messaoudi

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  1. Salim A. Messaoudi
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Correspondence to Salim A. Messaoudi.

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Messaoudi, S.A. General Decay of Solutions of a Weak Viscoelastic Equation. Arab J Sci Eng 36, 1569–1579 (2011). https://doi.org/10.1007/s13369-011-0132-y

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  • DOI: https://doi.org/10.1007/s13369-011-0132-y

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