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Well-Posedness and Dynamical Properties for Extensible Beams with Nonlocal Frictional Damping and Polynomial Nonlinearity

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Abstract

This paper is concerned with extensible beams with nonlocal frictional damping and polynomial nonlinearity. By using semigroup theory, potential well method, and energy method, the well-posedness and the conditions on global existence and finite time blow-up of solutions are studied. Moreover, the upper bound of blow-up time is also given by using ordinary differential inequalities.

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Acknowledgements

The authors convey thanks to the reviewers for their helpful comments and suggestions which improve this paper greatly.

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  1. School of Mathematics and Statistics, Southwest University, Chongqing, 400715, People’s Republic of China

    Kailun Chen & Jun Zhou

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  1. Kailun Chen
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  2. Jun Zhou
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Correspondence to Jun Zhou.

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This work is supported by Natural Science Foundation of Chongqing (CSTB2022NSCQ-MSX1674).

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Chen, K., Zhou, J. Well-Posedness and Dynamical Properties for Extensible Beams with Nonlocal Frictional Damping and Polynomial Nonlinearity. Appl Math Optim 88, 92 (2023). https://doi.org/10.1007/s00245-023-10070-w

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