TY - JOUR
T1 - Analyticity and Differentiability of Semigroups Associated with Elastic Systems with Damping and Gyroscopic Forces
AU - Liu, Kangsheng
AU - Liu, Zhuangyi
N1 - Funding Information:
partially by the National Natural Science Foundation of China Grant
PY - 1997/12/10
Y1 - 1997/12/10
N2 - In this paper, we consider a second order variational evolution equation in a Hilbert space, which can model an elastic system with damping and gyroscopic forces. A new form of the corresponding first order evolution equation is introduced, and its well-posedness is proved by means of the semigroup theory. We give sufficient conditions for analyticity and differentiablity of the associated semigroup. The results are applied to several PDEs with discontinuous coefficients and mechanical boundary conditions. It is proved that Russell's spacial hysteresis model of a vibrating beam [22] is associated with an exponentially stable, analytic semigroup.
AB - In this paper, we consider a second order variational evolution equation in a Hilbert space, which can model an elastic system with damping and gyroscopic forces. A new form of the corresponding first order evolution equation is introduced, and its well-posedness is proved by means of the semigroup theory. We give sufficient conditions for analyticity and differentiablity of the associated semigroup. The results are applied to several PDEs with discontinuous coefficients and mechanical boundary conditions. It is proved that Russell's spacial hysteresis model of a vibrating beam [22] is associated with an exponentially stable, analytic semigroup.
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U2 - 10.1006/jdeq.1997.3331
DO - 10.1006/jdeq.1997.3331
M3 - Article
AN - SCOPUS:0011608163
SN - 0022-0396
VL - 141
SP - 340
EP - 355
JO - Journal of Differential Equations
JF - Journal of Differential Equations
IS - 2
ER -