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Eventual regularity of a wave equation with boundary dissipation
1.  Department of Mathematics, Zhejiang University, Hangzhou 310027, China 
2.  School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China 
3.  Institut de Recherche Mathématique Avancée, Université Louis Pasteur de Strasbourg, 7 rue RenéDescartes, 67084 Strasbourg 
References:
[1] 
C. J. K. Batty, Differentiability and growth bounds of solutions of delay equations, J. Math. Anal. Appl., 299 (2004), 133146. doi: 10.1016/j.jmaa.2004.04.063. 
[2] 
C. J. K. Batty, Differentiability of perturbed semigroups and delay semigroups, in "Perspectives in Operator Theory," Banach Center Publ., 75, Polish Acad. Sci., Warsaw, (2007), 3953. 
[3] 
G. Chen and J. Zhou, "Vibration and Damping in Distributed Systems. Vol. I. Analysis, Estimation, Attenuation, and Design," Studies in Advanced Mathematics, CRC Press, Boca Raton, FL, 1993. 
[4] 
G. Di Blasio, Differentiability of the solution semigroup for delay differential equations, in "Evolution Equations," Lecture Notes in Pure and Appl. Math., 234, Dekker, New York, (2003), 147158. 
[5] 
G. Di Blasio, K. Kunisch and E. Sinestrari, Stability for abstract linear functional differential equations, Israel J. Math., 50 (1985), 231263. 
[6] 
B. D. Doytchinov, W. J. Hrusa and S. J. Watson, On perturbations of differentiable semigroups, Semigroup Forum, 54 (1997), 100111. doi: 10.1007/BF02676591. 
[7] 
R. H. Fabiano and K. Ito, Semigroup theory in linear viscoelasticity: Weakly and strongly singular kernels, in "Control and Estimation of Distributed Parameter Systems" (Vorau, 1988), Internat. Ser. Numer. Math., 91, Birkhäuser, Basel, (1989), 109121. 
[8] 
K. Liu and Z. Liu, Analyticity and differentiability of semigroups associated with elastic systems with damping and gyroscopic forces, J. Differential Equations, 141 (1997), 340355. 
[9] 
A. Pazy, "Semigroups of Linear Operators and Applications to Partial Differential Equations," Applied Mathematical Sciences, 44, SpringerVerlag, New York, 1983. 
[10] 
M. Renardy, On the stability of differentiability of semigroups, Semigroup Forum, 51 (1995), 343346. 
[11] 
X. Yu, Differentiability of the agedependent population system with time delay in the birth process, J. Math. Anal. Appl., 303 (2005), 576584. 
[12] 
X. Yu and K. Liu, Eventual differentiability of functional differential equations in Banach spaces, J. Math. Anal. Appl., 327 (2007), 792800. 
[13] 
L. Zhang, Differentiability of the population semigroup, (Chinese) J. Systems Sci. Math. Sci., 8 (1988), 181187. 
show all references
References:
[1] 
C. J. K. Batty, Differentiability and growth bounds of solutions of delay equations, J. Math. Anal. Appl., 299 (2004), 133146. doi: 10.1016/j.jmaa.2004.04.063. 
[2] 
C. J. K. Batty, Differentiability of perturbed semigroups and delay semigroups, in "Perspectives in Operator Theory," Banach Center Publ., 75, Polish Acad. Sci., Warsaw, (2007), 3953. 
[3] 
G. Chen and J. Zhou, "Vibration and Damping in Distributed Systems. Vol. I. Analysis, Estimation, Attenuation, and Design," Studies in Advanced Mathematics, CRC Press, Boca Raton, FL, 1993. 
[4] 
G. Di Blasio, Differentiability of the solution semigroup for delay differential equations, in "Evolution Equations," Lecture Notes in Pure and Appl. Math., 234, Dekker, New York, (2003), 147158. 
[5] 
G. Di Blasio, K. Kunisch and E. Sinestrari, Stability for abstract linear functional differential equations, Israel J. Math., 50 (1985), 231263. 
[6] 
B. D. Doytchinov, W. J. Hrusa and S. J. Watson, On perturbations of differentiable semigroups, Semigroup Forum, 54 (1997), 100111. doi: 10.1007/BF02676591. 
[7] 
R. H. Fabiano and K. Ito, Semigroup theory in linear viscoelasticity: Weakly and strongly singular kernels, in "Control and Estimation of Distributed Parameter Systems" (Vorau, 1988), Internat. Ser. Numer. Math., 91, Birkhäuser, Basel, (1989), 109121. 
[8] 
K. Liu and Z. Liu, Analyticity and differentiability of semigroups associated with elastic systems with damping and gyroscopic forces, J. Differential Equations, 141 (1997), 340355. 
[9] 
A. Pazy, "Semigroups of Linear Operators and Applications to Partial Differential Equations," Applied Mathematical Sciences, 44, SpringerVerlag, New York, 1983. 
[10] 
M. Renardy, On the stability of differentiability of semigroups, Semigroup Forum, 51 (1995), 343346. 
[11] 
X. Yu, Differentiability of the agedependent population system with time delay in the birth process, J. Math. Anal. Appl., 303 (2005), 576584. 
[12] 
X. Yu and K. Liu, Eventual differentiability of functional differential equations in Banach spaces, J. Math. Anal. Appl., 327 (2007), 792800. 
[13] 
L. Zhang, Differentiability of the population semigroup, (Chinese) J. Systems Sci. Math. Sci., 8 (1988), 181187. 
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