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AIMS Mathematics

2018, Volume 3, Issue 4: 608-624. doi: 10.3934/Math.2018.4.608
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Research article

Existence result for a nonlinear nonlocal system modeling suspension bridges

  • College of Mathematics and Information Science, Hebei University, Baoding, China
  • Received: 07 September 2018 Accepted: 28 November 2018 Published: 04 December 2018

  • MSC : 35G61, 74B20

  • A nonlinear nonlocal partial di erential system modeling suspension bridge is considered. We analyze the well-posedness of the "hyperbolic" type system through a Galerkin procedure. A correspond linear problem admits a unique solution, which makes us find that the original system also has a solution with high regularity.

    Citation: Yongda Wang. Existence result for a nonlinear nonlocal system modeling suspension bridges[J]. AIMS Mathematics, 2018, 3(4): 608-624. doi: 10.3934/Math.2018.4.608

    Related Papers:

  • A nonlinear nonlocal partial di erential system modeling suspension bridge is considered. We analyze the well-posedness of the "hyperbolic" type system through a Galerkin procedure. A correspond linear problem admits a unique solution, which makes us find that the original system also has a solution with high regularity.


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    [1] G. Arioli, F. Gazzola, On a nonlinear nonlocal hyperbolic system modeling suspension bridges, Milan J. Math., 83 (2015), 211-236.
    [2] G. Arioli, F. Gazzola, Torsional instability in suspension bridges: the Tacoma Narrows Bridge case, Commun. Nonlinear Sci., 42 (2017), 342-357.
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    [4] C. Baiocchi, Soluzioni ordinarie e generalizzate del problema di Cauchy per equazioni differenziali astratte non lineari del secondo ordine in spazi di Hilbert, Ricerche Mat., 16 (1967), 27-95.
    [5] H. Brezis, Operateurs maximaux monotones, North-Holland, Amsterdam, 1973.
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    [7] R. Courant, D. Hilbert, Methods of mathematical physics, Intersciences Publishers, New York, 1953.
    [8] A. Falocchi, Structural instability in a simplified nonlinear model for suspension bridges, AIMETA 2017-Proceedings of the 23rd Conference of the Italian Association of Theoretical and Applied Mechanics, 4 (2017), 746-759.
    [9] A. Falocchi, Torsional instability and sensitivity analysis in a suspension bridge model related to the Melan equation, Commun. Nonlinear Sci., 67 (2019), 60-75.
    [10] A. Ferrero, F. Gazzola, A partially hinged rectangular plate as a model for suspension bridges, Discrete Cont. Dyn-A, 35 (2015), 5879-5908.
    [11] R. Temam, Infinite-dimensional dynamical systems in mechanics and physics, Applied Mathematical Sciences, 68, Springer, 1997.
    [12] Y. Wang, Finite time blow-up and global solutions for fourth order damped wave equations, J. Math. Anal. Appl., 418 (2014), 713-733.
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  • © 2018 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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