AIMS Mathematics, 2017, 2(3): 557-561. doi: 10.3934/Math.2017.2.557.

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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

We provide a new proof of the upper-semicontinuity property for the global attractorsadmitted 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 phasespace in terms of the perturbation parameter. This result strengthens the recent work by Y. Wang andC. Zhong [7].
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Keywords Upper-semicontinuity; global attractor; strongly damped wave equation

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

References

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  • 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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Copyright Info: © 2017, Joseph L. Shomberg, licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

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