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General decay and blow up of solutions for the Kirchhoff plate equation with dynamic boundary conditions, delay and source terms

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Abstract

In this paper, we consider a viscoelastic Kirchhoff plate equation with dynamic boundary conditions, delay and source terms acting on the boundary. Under suitable assumptions on the functions M, \(\sigma \) and g, first, we obtain global existence of solution by using the potential well method and introducing suitable energy and Lyapunov functionals to establish general decay result. Finally, 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).

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Authors and Affiliations

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

    Houria Kamache & Nouri Boumaza

  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

    Houria Kamache, Nouri Boumaza & Billel Gheraibia

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  1. Houria Kamache
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  2. Nouri Boumaza
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Correspondence to Nouri Boumaza.

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Kamache, H., Boumaza, N. & Gheraibia, B. General decay and blow up of solutions for the Kirchhoff plate equation with dynamic boundary conditions, delay and source terms. Z. Angew. Math. Phys. 73, 76 (2022). https://doi.org/10.1007/s00033-022-01700-4

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  • DOI: https://doi.org/10.1007/s00033-022-01700-4

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