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AIMS Mathematics

2017, Volume 2, Issue 3: 557-561. doi: 10.3934/Math.2017.2.557
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Research article

On the upper semicontinuity of global attractors for damped wave equations

  • Department of Mathematics and Computer Science, Providence College, 1 Cunningham Square, Providence, Rhode Island 02918, USA
  • Received: 17 July 2017 Accepted: 07 August 2017 Published: 14 September 2017

  • We provide a new proof of the upper-semicontinuity property for the global attractors admitted by the solution operators associated with some strongly damped wave equations. In particular, we demonstrate an explicit control over semidistances between trajectories in the weak energy phase space in terms of the perturbation parameter. This result strengthens the recent work by Y. Wang and C. Zhong [7].

    Citation: Joseph L. Shomberg. On the upper semicontinuity of global attractors for damped wave equations[J]. AIMS Mathematics, 2017, 2(3): 557-561. doi: 10.3934/Math.2017.2.557

    Related Papers:

  • We provide a new proof of the upper-semicontinuity property for the global attractors admitted by the solution operators associated with some strongly damped wave equations. In particular, we demonstrate an explicit control over semidistances between trajectories in the weak energy phase space in terms of the perturbation parameter. This result strengthens the recent work by Y. Wang and C. Zhong [7].


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    [1] A. V. Babin and M. I. Vishik, Attractors of evolution equations, North-Holland, Amsterdam, 1992.
    [2] Alexandre N. Carvalho and Jan W. Cholewa, Attractors for strongly damped wave equations with critical nonlinearities, Pacific J. Math. 207 (2002), 287-310.
    [3] Alexandre N. Carvalho and Jan W. Cholewa, Local well posedness for strongly damped wave equations with critical nonlinearities, Bull. Austral. Math. Soc. 66 (2002), 443-463.
    [4] V. Pata and M. Squassina, On the strongly damped wave equation, Comm. Math. Phys. 253 (2005), 511-533.
    [5] Vittorino Pata and Sergey Zelik, A remark on the damped wave equation, Commun. Pure Appl. Anal. 5 (2006), 609-614.
    [6] James C. Robinson, Infinite-dimensional dynamical systems, Cambridge Texts in Applied Mathematics, Cambridge University Press, Cambridge, 2001.
    [7] Yonghai Wang and Chengkui Zhong, Upper semicontinuity of global attractors for damped wave equations, Asymptot. Anal. 91 (2015), 1-10.
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  • © 2017 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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