AIMS Mathematics, 2018, 3(4): 608-624. doi: 10.3934/Math.2018.4.608

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Existence result for a nonlinear nonlocal system modeling suspension bridges

College of Mathematics and Information Science, Hebei University, Baoding, China

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.    

3. J. M. Ball, Initial-boundary value problems for an extensible beam, J. Math. Anal. Appl., 42 (1973), 61–90.    

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.

6. E. A. Coddington, N. Levinson, Theory of ordinary differential equations, McGraw-Hill, New York, 1955.

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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