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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 746893, 6 pages
http://dx.doi.org/10.1155/2013/746893
Research Article

Existence of Mild Solutions for the Elastic Systems with Structural Damping in Banach Spaces

1Department of Mathematics, Lanzhou Jiaotong University, Lanzhou 730070, China
2Department of Mathematics, Northwest Normal University, Lanzhou 730070, China

Received 2 November 2012; Revised 6 January 2013; Accepted 16 January 2013

Academic Editor: Ferenc Hartung

Copyright © 2013 Hongxia Fan et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. G. Chen and D. L. Russell, “A mathematical model for linear elastic systems with structural damping,” Quarterly of Applied Mathematics, vol. 39, no. 4, pp. 433–454, 1982. View at MathSciNet
  2. F. L. Huang, “On the holomorphic property of the semigroup associated with linear elastic systems with structural damping,” Acta Mathematica Scientia, vol. 5, no. 3, pp. 271–277, 1985. View at Zentralblatt MATH · View at MathSciNet
  3. F. Huang, “A problem for linear elastic systems with structural damping,” Acta Math-Ematica Scientia, vol. 6, no. 1, pp. 101–107, 1986 (Chinese).
  4. S. Chen and R. Triggiani, “Proof of extensions of two conjectures on structural damping for elastic systems: the systems: the case 1/2α1,” Pacific Journal of Mathematics, vol. 136, no. 1, pp. 15–55, 1989.
  5. S. Chen and R. Triggiani, “Gevrey class semigroups arising from elastic systems with gentle dissipation: the case 0<α<1/2,” Proceedings of the American Mathmematical Society, vol. 110, no. 2, pp. 401–415, 1990.
  6. F. L. Huang, “On the mathematical model for linear elastic systems with analytic damping,” SIAM Journal on Control and Optimization, vol. 26, no. 3, pp. 714–724, 1988. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. K. Liu and Z. Liu, “Analyticity and differentiability of semigroups associated with elastic systems with damping and gyroscopic forces,” Journal of Differential Equations, vol. 141, no. 2, pp. 340–355, 1997. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. F. L. Huang and K. S. Liu, “Holomorphic property and exponential stability of the semigroup associated with linear elastic systems with damping,” Annals of Differential Equations, vol. 4, no. 4, pp. 411–424, 1988. View at Zentralblatt MATH · View at MathSciNet
  9. F. L. Huang, Y. Z. Huang, and F. M. Guo, “Holomorphic and differentiable properties of the C0-semigroup associated with the Euler-Bernoulli beam equations with structural damping,” Science in China A, vol. 35, no. 5, pp. 547–560, 1992. View at MathSciNet
  10. F. L. Huang, K. S. Liu, and G. Chen, “Differentiability of the semigroup associated with a structural damping model,” in Proceedings of the 28th IEEE Conference on Decision and Control (IEEE-CDC 1989), pp. 2034–2038, Tampa, Fla, USA, 1989. View at MathSciNet
  11. K.-J. Engel and R. Nagel, One-Parameter Semigroups for Linear Evolution Equations, Springer, New York, NY, USA, 2000.
  12. A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer, Berlin, Germany, 1983. View at Publisher · View at Google Scholar · View at MathSciNet
  13. D. Henry, Geometric Theory of Semilinear Parabolic Equations, Springer, New York, NY, USA, 1981. View at MathSciNet