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A viscoelastic wave equation with delay and variable exponents: existence and nonexistence

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Abstract

This article deals with the existence and nonexistence of solutions for a viscoelastic wave equation with time delay and variable exponents on the damping and on source term. Firstly, we get the existence of weak solutions by combining the Banach contraction mapping principle and the Faedo–Galerkin method under suitable assumptions on the variable exponents \(m\left( \cdot \right) \) and \(p\left( \cdot \right) \). For nonincreasing positive function g, we obtain the nonexistence of solutions with negative initial energy in appropriate conditions.

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Acknowledgements

The authors would like to thank the referees for all insightful comments, which allow us to clarify some points in our original version.

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Authors and Affiliations

  1. Department of Mathematics, Dicle University, Diyarbakir, Turkey

    Hazal Yüksekkaya & Erhan Pişkin

  2. Department of Mathematics, Fluminense Federal University, Volta Redonda, RJ, Brazil

    Jorge Ferreira

  3. Department of Mathematics, Jahrom University, P.O.Box: 74137-66171, Jahrom, Iran

    Mohammad Shahrouzi

Authors
  1. Hazal Yüksekkaya
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  2. Erhan Pişkin
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  3. Jorge Ferreira
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  4. Mohammad Shahrouzi
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Correspondence to Mohammad Shahrouzi.

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Yüksekkaya, H., Pişkin, E., Ferreira, J. et al. A viscoelastic wave equation with delay and variable exponents: existence and nonexistence. Z. Angew. Math. Phys. 73, 133 (2022). https://doi.org/10.1007/s00033-022-01776-y

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  • DOI: https://doi.org/10.1007/s00033-022-01776-y

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