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Asymptotic Behavior for a Viscoelastic Kirchhoff-Type Equation with Delay and Source Terms

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Abstract

In this work, we consider a nonlinear viscoelastic Kirchhoff-type equation with delay and source terms in a bounded domain. Under an hypothesis between the weight of the delay term in the feedback and the weight of the weak damping term, we obtain a global existence of solutions and established the general decay rate, also we prove the finite time blow-up result of solutions with negative initial energy.

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Acknowledgements

This work was supported by the Directorate-General for Scientific Research and Technological Development, Algeria (DGRSDT). The authors would like to thank the referees and the handling editor for their helpful suggestions upon which this paper was revised.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, Larbi Tebessi University, Tebessa, Algeria

    Nouri Boumaza & Meriem Saker

  2. Department of Mathematics and Computer Science, Larbi Ben M’Hidi University, Oum El-Bouaghi, Algeria

    Billel Gheraibia

  3. Laboratory of Mathematics, Informatics and Systems (LAMIS), Larbi Tebessi University, Tebessa, Algeria

    Nouri Boumaza, Meriem Saker & Billel Gheraibia

Authors
  1. Nouri Boumaza
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  2. Meriem Saker
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  3. Billel Gheraibia
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Correspondence to Nouri Boumaza.

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Boumaza, N., Saker, M. & Gheraibia, B. Asymptotic Behavior for a Viscoelastic Kirchhoff-Type Equation with Delay and Source Terms. Acta Appl Math 171, 18 (2021). https://doi.org/10.1007/s10440-021-00387-5

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  • DOI: https://doi.org/10.1007/s10440-021-00387-5

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