TY - JOUR
T1 - Note on stability of an abstract coupled hyperbolic-parabolic system
T2 - Singular case
AU - Ammari, Kaïs
AU - Liu, Zhuangyi
AU - Shel, Farhat
N1 - Publisher Copyright:
© 2023 Elsevier Ltd
PY - 2023/7
Y1 - 2023/7
N2 - In this paper we try to complete the stability analysis for an abstract system of coupled hyperbolic and parabolic equations utt+Au−Aαw=0,wt+Aαut+Aβw=0,u(0)=u0,ut(0)=u1,w(0)=w0,where A is a self-adjoint, positive definite operator on a complex Hilbert space H, and (α,β)∈[0,1]×[0,1], which is considered in Ammar-Khodja et al. (1999), and after, in Hao et al. (2013). Our contribution is to identify a fine scale of polynomial stability of the solution in the region S3:=(α,β)∈[0,1]×[0,1];β<2α−1 taking into account the presence of a singularity at zero.
AB - In this paper we try to complete the stability analysis for an abstract system of coupled hyperbolic and parabolic equations utt+Au−Aαw=0,wt+Aαut+Aβw=0,u(0)=u0,ut(0)=u1,w(0)=w0,where A is a self-adjoint, positive definite operator on a complex Hilbert space H, and (α,β)∈[0,1]×[0,1], which is considered in Ammar-Khodja et al. (1999), and after, in Hao et al. (2013). Our contribution is to identify a fine scale of polynomial stability of the solution in the region S3:=(α,β)∈[0,1]×[0,1];β<2α−1 taking into account the presence of a singularity at zero.
KW - Hyperbolic-parabolic system
KW - Stability
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U2 - 10.1016/j.aml.2023.108599
DO - 10.1016/j.aml.2023.108599
M3 - Article
AN - SCOPUS:85147247400
SN - 0893-9659
VL - 141
JO - Applied Mathematics Letters
JF - Applied Mathematics Letters
M1 - 108599
ER -