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Exponential decay of solutions to a class of fourth-order nonlinear hyperbolic equations modeling the oscillations of suspension bridges

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Języki publikacji
EN
Abstrakty
EN
This paper is concerned with a class of fourth-order nonlinear hyperbolic equations subject to free boundary conditions that can be used to describe the nonlinear dynamics of suspension bridges.
Rocznik
Strony
239--255
Opis fizyczny
Bibliogr. 23 poz.
Twórcy
autor
  • Northwest Minzu University, College of Mathematics and Computer Science, No. 1, Northwest New Village, Lanzhou 730030, P.R. China
  • Sichuan University, College of Mathematics, No. 24, South Section 1, Yihuan Road, Chengdu 610065, P.R. China
autor
  • Harbin Engineering University, College of Mathematical Sciences, No. 145, Nantong Street, Harbin 150001, P.R. China
Bibliografia
  • [1] R.A. Adams, Sobolev Spaces, Academic Press, New York, 1975.
  • [2] S. Baraket, V.D. Radulescu, Combined effects of concave-convex nonlinearities in a fourth-order problem with variable exponent, Adv. Nonlinear Stud. 16 (2016), 409–419.
  • [3] J.M.W. Brownjohn, Observations on non-linear dynamic characteristics of suspension bridges, Earthquake Engng. Struct. Dyn. 23 (1994), 1351–1367.
  • [4] A. Ferrero, F. Gazzola, A partially hinged rectangular plate as a model for suspension bridges, Discrete Contin. Dyn. Syst. 35 (2015), 5879–5908.
  • [5] F. Gazzola, Nonlinearity in oscillating bridges, Electron. J. Differential Equations 211 (2013), 1642–1654.
  • [6] W. Lacarbonara, Nonlinear Structural Mechanics: Theory, Dynamical Phenomena and Modeling, Springer, New York, 2013.
  • [7] A.C. Lazer, P.J. McKenna, Large scale oscillatory behaviour in loaded asymmetric systems, Ann. Inst. H. Poincaré Anal. Non Linéaire 4 (1987), 243–274.
  • [8] W. Lian, J. Wang, R. Xu, Global existence and blow up of solutions for pseudo-parabolic equation with singular potential, J. Differential Equations 269 (2020), 4914–4959.
  • [9] W. Lian, R. Xu, Global well-posedness of nonlinear wave equation with weak and strong damping terms and logarithmic source term, Adv. Nonlinear Anal. 9 (2020), 612–632.
  • [10] Y. Liu, J. Zhao, On potential wells and applications to semilinear hyperbolic equations and parabolic equations, Nonlinear Anal. 64 (2006), 2665–2687.
  • [11] P.J. McKenna, W. Walter, Nonlinear oscillations in a suspension bridge, Arch. Ration. Mech. Anal. 98 (1987), 167–177.
  • [12] P.J. McKenna, W. Walter, Travelling waves in a suspension bridge, SIAM J. Appl. Math. 50 (1990), 703–715.
  • [13] A. Mohammed, V.D. Radulescu, A. Vitolo, Blow-up solutions for fully nonlinear equations: Existence, asymptotic estimates and uniqueness, Adv. Nonlinear Stud. 9 (2020), 39–64.
  • [14] L.E. Payne, D.H. Sattinger, Sadle points and instability of nonlinear hyperbolic equations, Israel J. Math. 22 (1975), 273–303.
  • [15] R.H. Plaut, F.M. Davis, Sudden lateral asymmetry and torsional oscillations of section models of suspension bridges, J. Sound Vib. 307 (2007), 894–905.
  • [16] V. Radulescu, Nonlinear Analysis – Theory and Methods, Springer, New York, 2019.
  • [17] D.H. Sattinger, On global solution of nonlinear hyperbolic equations, Arch. Rational Mech. Anal. 30 (1968), 148–172.
  • [18] E. Ventsel, T. Krauthammer, Thin Plates and Shells: Theory, Analysis, and Applications, Marcel Dekker, New York, 2001.
  • [19] Y.Wang, Finite time blow-up and global solutions for fourth order damped wave equations, J. Math. Anal. Appl. 418 (2014), 713–733.
  • [20] R. Xu, W. Lian, Y. Niu, Global well-posedness of coupled parabolic systems, Sci. China Math. 63 (2020), 321–356.
  • [21] R. Xu, J. Su, Global existence and finite time blow-up for a class of semilinear pseudo-parabolic equations, J. Funct. Anal. 264 (2013), 2732–2763.
  • [22] R. Xu, X. Wang, Y. Yang, S. Chen, Global solutions and finite time blow-up for fourth order nonlinear damped wave equation, J. Math. Phys. 59 (2018), 061503.
  • [23] R. Xu, M. Zhang, S. Chen, Y. Yang, J. Shen, The initial-boundary value problems for a class of six order nonlinear wave equation, Discrete Contin. Dyn. Syst. 37 (2017), 5631–5649.
Uwagi
Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-86e0d9f5-c3c7-4f97-a35f-3079687a4143
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