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A study on decay mild solutions for damped elastic systems in Banach spaces

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Abstract

The goal of this paper is to consider damped elastic systems with nonlocal conditions in the framework of Banach spaces. Our first aim is to investigate the existence of mild solutions to damped elastic systems by means of fixed point for condensing maps avoiding the hypothesis of compactness on the semigroup. The second step of the paper is to study the existence of decay mild solutions to the mentioned problems. The obtained results can be applied to the nonlinear vibration equation of structural damping elastic beams with nonlocal conditions.

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Acknowledgements

We would like to thank the referees and the editor greatly for the careful review and the important suggestions to this paper. This work is supported by the National Natural Science Foundation of China (Grant Nos. 12061062, 11661071). Science Research Project for Colleges and Universities of Gansu Province (No. 2022A-010).

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  1. Department of Mathematics, Northwest Normal University, Lanzhou, 730070, People’s Republic of China

    Haide Gou & Weifeng Ma

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  1. Haide Gou
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Supported by the National Natural Science Foundation of China (Grant Nos. 12061062, 11661071). Science Research Project for Colleges and Universities of Gansu Province (No. 2022A-010).

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Gou, H., Ma, W. A study on decay mild solutions for damped elastic systems in Banach spaces. Monatsh Math 202, 515–539 (2023). https://doi.org/10.1007/s00605-023-01883-6

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