Abstract
In this paper, we study the singular limit dynamics of two wave equations connected in parallel when the spring coefficient \(\alpha \) tends to infinity. Firstly, we prove the existence, finiteness of fractal dimension and smoothness of global attractors. We establishes that the singular limit of two wave equations connected in parallel is a single wave equation when \(\alpha \rightarrow +\infty \). We also prove of upper-semicontinuity of global attractors when \(\alpha \rightarrow +\infty \).
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Acknowledgements
We would like to thank the anonymous referee for constructive comments and for proposing an interesting and challenging problem.
Funding
A. J. A. Ramos thanks the CNPq for financial support through the project: “Asymptotic stabilization and numerical treatment for carbon nanotubes” - CNPq Grant 310729/2019-0. M. L. Santos wants to thank CNPq for financial support through the projects: CNPq Grant 303026/2018-9 and CNPq Grant Pós-doc Sênior /PDS114563/ 2018-7.
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Freitas, M.M., Caljaro, R.Q., Santos, M.L. et al. Singular Limit Dynamics and Attractors for Wave Equations Connected in Parallel. Appl Math Optim 85, 9 (2022). https://doi.org/10.1007/s00245-022-09849-0
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DOI: https://doi.org/10.1007/s00245-022-09849-0