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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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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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Keywords

  • Acoustic boundary conditions
  • blow up
  • polynomial decay
  • variable coefficients
  • viscoelastic wave equation

MR(2010) Subject Classification

  • 35L45
  • 35L70
  • 35B40