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Polynomial decay and blow up of solutions for variable coefficients viscoelastic wave equation with acoustic boundary conditions

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Abstract

A variable coefficient viscoelastic wave equation with acoustic boundary conditions and nonlinear source term is considered. Under suitable conditions on the initial data and the relaxation function g, we show the polynomial decay of the energy solution and the blow up of solutions by energy methods. The estimates for the lifespan of solutions are also given.

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Authors and Affiliations

  1. Laboratory of Computer Sciences and Mathematics, Faculty of Sciences, University of Laghouat, P.O. BOX 37G, Laghouat, 03000, Algeria

    Yamna Boukhatem & Benyattou Benabderrahmane

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  1. Yamna Boukhatem
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  2. Benyattou Benabderrahmane
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Correspondence to Yamna Boukhatem.

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Boukhatem, Y., Benabderrahmane, B. Polynomial decay and blow up of solutions for variable coefficients viscoelastic wave equation with acoustic boundary conditions. Acta. Math. Sin.-English Ser. 32, 153–174 (2016). https://doi.org/10.1007/s10114-016-5093-3

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  • DOI: https://doi.org/10.1007/s10114-016-5093-3

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