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Exponential stability of a general network of 1-d thermoelastic rods
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 René-Descartes, 67084 Strasbourg |
References:
[1] |
C. J. K. Batty, Differentiability and growth bounds of solutions of delay equations, J. Math. Anal. Appl., 299 (2004), 133-146.
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), 39-53. |
[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), 147-158. |
[5] |
G. Di Blasio, K. Kunisch and E. Sinestrari, Stability for abstract linear functional differential equations, Israel J. Math., 50 (1985), 231-263. |
[6] |
B. D. Doytchinov, W. J. Hrusa and S. J. Watson, On perturbations of differentiable semigroups, Semigroup Forum, 54 (1997), 100-111.
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), 109-121. |
[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), 340-355. |
[9] |
A. Pazy, "Semigroups of Linear Operators and Applications to Partial Differential Equations," Applied Mathematical Sciences, 44, Springer-Verlag, New York, 1983. |
[10] |
M. Renardy, On the stability of differentiability of semigroups, Semigroup Forum, 51 (1995), 343-346. |
[11] |
X. Yu, Differentiability of the age-dependent population system with time delay in the birth process, J. Math. Anal. Appl., 303 (2005), 576-584. |
[12] |
X. Yu and K. Liu, Eventual differentiability of functional differential equations in Banach spaces, J. Math. Anal. Appl., 327 (2007), 792-800. |
[13] |
L. Zhang, Differentiability of the population semigroup, (Chinese) J. Systems Sci. Math. Sci., 8 (1988), 181-187. |
show all references
References:
[1] |
C. J. K. Batty, Differentiability and growth bounds of solutions of delay equations, J. Math. Anal. Appl., 299 (2004), 133-146.
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), 39-53. |
[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), 147-158. |
[5] |
G. Di Blasio, K. Kunisch and E. Sinestrari, Stability for abstract linear functional differential equations, Israel J. Math., 50 (1985), 231-263. |
[6] |
B. D. Doytchinov, W. J. Hrusa and S. J. Watson, On perturbations of differentiable semigroups, Semigroup Forum, 54 (1997), 100-111.
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), 109-121. |
[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), 340-355. |
[9] |
A. Pazy, "Semigroups of Linear Operators and Applications to Partial Differential Equations," Applied Mathematical Sciences, 44, Springer-Verlag, New York, 1983. |
[10] |
M. Renardy, On the stability of differentiability of semigroups, Semigroup Forum, 51 (1995), 343-346. |
[11] |
X. Yu, Differentiability of the age-dependent population system with time delay in the birth process, J. Math. Anal. Appl., 303 (2005), 576-584. |
[12] |
X. Yu and K. Liu, Eventual differentiability of functional differential equations in Banach spaces, J. Math. Anal. Appl., 327 (2007), 792-800. |
[13] |
L. Zhang, Differentiability of the population semigroup, (Chinese) J. Systems Sci. Math. Sci., 8 (1988), 181-187. |
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