TY - JOUR
T1 - Stability of an abstract system of coupled hyperbolic and parabolic equations
AU - Hao, Jianghao
AU - Liu, Zhuangyi
PY - 2013/8/1
Y1 - 2013/8/1
N2 - In this paper, we provide a complete stability analysis for an abstract system of coupled hyperbolic and parabolic equations where A is a self-adjoint, positive definite operator on a Hilbert space H. For (α β) ∈ [0,1] × [0,1], the region of exponential stability had been identified in Ammar-Khodja et al. (ESAIM Control Optim Calc Var 4:577-593,1999). Our contribution is to show that the rest of the region can be classified as region of polynomial stability and region of instability. Moreover, we obtain the optimality of the order of polynomial stability.
AB - In this paper, we provide a complete stability analysis for an abstract system of coupled hyperbolic and parabolic equations where A is a self-adjoint, positive definite operator on a Hilbert space H. For (α β) ∈ [0,1] × [0,1], the region of exponential stability had been identified in Ammar-Khodja et al. (ESAIM Control Optim Calc Var 4:577-593,1999). Our contribution is to show that the rest of the region can be classified as region of polynomial stability and region of instability. Moreover, we obtain the optimality of the order of polynomial stability.
KW - Exponentialstability
KW - Hyperbolic-parabolic equation
KW - Polynomial stability
KW - Semigroup
UR - http://www.scopus.com/inward/record.url?scp=84880582899&partnerID=8YFLogxK
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U2 - 10.1007/s00033-012-0274-0
DO - 10.1007/s00033-012-0274-0
M3 - Article
AN - SCOPUS:84880582899
SN - 0044-2275
VL - 64
SP - 1145
EP - 1159
JO - Zeitschrift fur Angewandte Mathematik und Physik
JF - Zeitschrift fur Angewandte Mathematik und Physik
IS - 4
ER -