A Study on Damped Elastic Systems in Banach Spaces

References

• Chen, G., Russell, D. L. (1982). A mathematical model for linear elastic systems with structural damping. Quart. Appl. Math. 39(4):433–454. DOI: 10.1090/qam/644099.
   Web of Science ®Google Scholar
• Huang, F. L. (1985). On the holomorphic property of the semigroup associated with linear elastic systems with structural damping. Acta Math. Sci. 5(3):271–277. DOI: 10.1016/S0252-9602(18)30548-4.
   Web of Science ®Google Scholar
• Huang, F. (1986). A problem for linear elastic systems with structural damping. Acta Math. Sci. 6(1):101–107. (in Chinese).
   Google Scholar
• Chen, S., Triggiani, R. (1989). Proof of extensions of two conjectures on structural damping for elastic systems: the systems: the case 12≤α≤1. Pac. J. Math. 136(1):15–55. DOI: 10.2140/pjm.1989.136.15.
   Web of Science ®Google Scholar
• Chen, S., Triggiani, R. (1990). Gevrey class semigroups arising from elastic systems with gentle dissipation: the case 0<α<12,. Proc. Am. Math. Soc. 110(2):401–415.
   Web of Science ®Google Scholar
• Huang, F. L. (1988). On the mathematical model for linear elastic systems with analytic damping. SIAM J. Control Optim. 26(3):714–724. DOI: 10.1137/0326041.
   Web of Science ®Google Scholar
• Liu, K., Liu, Z. (1997). Analyticity and differentiability of semigroups associated with elastic systems with damping and gyroscopic forces. J. Differ. Eq. 141(2):340–355. DOI: 10.1006/jdeq.1997.3331.
   Web of Science ®Google Scholar
• Huang, F. L., Liu, K. S. (1988). Holomorphic property and exponential stability of the semigroup associated with linear elastic systems with damping. Ann. Differ. Eq. 4(4):411–424.
   Google Scholar
• Huang, F. L., Huang, Y. Z., Guo, F. M. (1992). Holomorphic and differentiable properties of the C0-semigroup associated with the Euler-Bernoulli beam equations with structural damping. Sci. China A 35(5):547–560.
   Google Scholar
• Huang, F. L., Liu, K. S., Chen, G. (1989). 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.
   Google Scholar
• Fan, H., Li, Y. (2014). Analyticity and exponential stability of semigroup for elastic systems with structural damping in Banach spaces. J. Math. Anal. Appl. 410(1):316–322. DOI: 10.1016/j.jmaa.2013.08.028.
   Web of Science ®Google Scholar
• Fan, H., Gao, F. (2014). Asymptotic stability of solutions to elastic systems with structural damping. Electron. J. Differ. Eq. 245:9.
   Google Scholar
• Fan, H., Li, Y., Chen, P. (2013). Existence of mild solutions for the elastic systems with structural damping in Banach spaces. Abstract Appl. Anal. 2013, 746893. DOI: 10.1155/2013/746893.
   Google Scholar
• Engel, K. J., Nagel, R. (2000). One-Parameter Semigroup for Linear Evolution Equations. New York, Berlin Heidelberg. Springer-Verlag.
   Google Scholar
• Luong, V. T., Tung, N. T. (2018). Exponential decay for elastic systems with structural damping and infinite delay. Appl. Anal. DOI: 10.1080/00036811.2018.1484907.
   Web of Science ®Google Scholar
• Luong, V. T., Tung, N. T. (2017). Decay mild solutions for elastic systems with structural damping involving nonlocal conditions. Vestnik St. Petersburg Univer. Math. 50(1):55–67. DOI: 10.3103/S1063454117010083.
   Web of Science ®Google Scholar
• Diagana, T. (2017). Well-posedness for some damped elastic systems in banach spaces. Appl. Math. Lett.71:74–80. DOI: 10.1016/j.aml.2017.03.016.
   Web of Science ®Google Scholar
• Graber, P. J., Lasiecka, I. (2014). Analyticity and Gevrey class regularity for a strongly damped wave equation with hyperbolic dynamic boundary conditions. Semigroup Forum 88(2):333–365. DOI: 10.1007/s00233-013-9534-3.
   Web of Science ®Google Scholar
• Liu, Z., Zhang, Q. (2015). A note on the polynomial stability of a weakly damped elastic abstract system. Z Angew. Math. Phys. 66(4):1799–1804. DOI: 10.1007/s00033-015-0517-y.
   Web of Science ®Google Scholar
• Batty, C. J. K., Chill, R., Srivastava, S. (2008). Maximal regularity for second order non-autonomous Cauchy problems. Studia Math. 189(3):205–223. DOI: 10.4064/sm189-3-1.
   Web of Science ®Google Scholar
• Chill, R., Srivastava, S. (2005). Lp-maximal regularity for second order Cauchy problems. Math. Z 251(4):751–781. DOI: 10.1007/s00209-005-0815-8.
   Web of Science ®Google Scholar
• Arendt, W., Chill, R., Fornaro, S., Poupaud, C. (2007). Lp maximal regularity for non-autonomous evolution equations. J. Differ. Eq. 237(1):1–26. DOI: 10.1016/j.jde.2007.02.010.
   Web of Science ®Google Scholar
• Charles, J. K. B., Chill, R., Srivastava, S. Maximal regularity in interpolation spaces for second order Cauchy problems, https://arxiv.org/abs/1404.2967v1.
   Google Scholar
• Pazy, A. (1983). Semigroups of Linear Operators and Applications to Partial Differential Equations. Berlin, Germany: Springer.
   Google Scholar
• Banas̀, J., Goebel, K. (1980). Measures of noncompactness in banach spaces. In: Lecture Notes in Pure and Applied Mathematics, Vol. 60, New York: Marcel Dekker
   Google Scholar
• Deimling, K. (1985). Nonlinear Functional Analysis. New York: Springer-Verlag.
   Google Scholar
• Y, L. (2005). Existence of solutions of initial value problems for abstract semilinear evolution equations. Acta Math. Sin. 48:1089–1094. (in Chinese).
   Google Scholar
• Heinz, H. P. (1983). On the behaviour of measure of noncompactness with respect to differentiation and integration of vector-valued functions. Nonlinear Anal. 7(12):1351–1371. DOI: 10.1016/0362-546X(83)90006-8.
   Web of Science ®Google Scholar