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Existence and general decay of solution for nonlinear viscoelastic two-dimensional beam with a nonlinear delay

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Abstract

We investigate the longitudinal and transversal vibrations of the viscoelastic beam with nonlinear tension and nonlinear delay term under the general decay rate for relaxation function. The existence theorem is proved by the Faedo–Galerkin method and using suitable Lyapunov functional to establish the general decay result.

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Acknowledgements

The authors would like to thank the anonymous referees for their valuable comments and suggestions. and express their gratitude to DGRSDT for the financial support.

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Correspondence to Billal Lekdim.

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Lekdim, B., Khemmoudj, A. Existence and general decay of solution for nonlinear viscoelastic two-dimensional beam with a nonlinear delay. Ricerche mat 73, 261–282 (2024). https://doi.org/10.1007/s11587-021-00598-w

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  • DOI: https://doi.org/10.1007/s11587-021-00598-w

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