[1] M. S. Alves, S. F. Arantes and J. E. M. Rivera, Exponential and
polynomial decay for an abstract hyperbolic-parabolic system
(preprinted).
[2] G. Avalos and I. Lasiecka, Exponential stability of a
thermoelastic system without mechanical dissipation, Rendiconti
dell’Istituto di Matematica dell’Universita di Trieste
28 (1997), 1-29.
[3] G. Avalos and I. Lasiecka, Exponential stability of a
thermoelastic system with free boundary conditions without mechanical
dissipation, SIAM Journal on Mathematical Analysis 29(1) (1998),
1-28.
DOI: https://doi.org/10.1137/S0036141096300823
[4] F. Dell’Oro, J. E. M. Rivera and V. Pata, Stability
properties of an abstract system with applications to linear
thermoelastic plates, Journal of Evolution Equations 13(4) (2013),
777-794.
DOI: https://doi.org/10.1007/s00028-013-0202-6
[5] K. J. Engel and R. Nagel, One-Parameter Semigroups for Linear
Evolution Equations, Springer, 2000.
DOI: https://doi.org/10.1007/b97696
[6] J. Hao and Z. Liu, Stability of an abstract system of coupled
hyperbolic and parabolic equations, Zeitschrift für Angewandte
Mathematik und Physik 64(4) (2013), 1145-1159.
DOI: https://doi.org/10.1007/s00033-012-0274-0
[7] V. Keyantuo, L. Tebou and M. Warma, A gevrey class semigroup for a
thermoelastic plate model with a fractional laplacian: between the
Euler-Bernoulli and Kirchhoff models, Discrete and Continuous
Dynamical System 40(5) (2020), 2875-2889.
DOI: https://doi.org/10.3934/dcds.2020152
[8] Z. Kuang, Z. Liu and H. D. F. Sare, Regularity analysis for an
abstract thermoelastic system with inertial term, ESAIM: Control,
Optimisation and Calculus of Variations 27(S24) (2021), 1-29.
DOI: https://doi.org/10.1051/cocv/2020075
[9] I. Lasiecka and R. Triggiani, Analyticity and lack thereof, of
thermo-elastic semigroups, ESAIM: Proceedings and Surveys 4 (1998),
199-222.
DOI: https://doi.org/10.1051/proc:1998029
[10] I. Lasiecka and R. Triggiani, Analyticity of thermo-elastic
semigroups with free boundary conditions, Annali della Scuola Normale
Superiore di Pisa - Classe di Scienze, Serie 4 27(3-4) (1998),
457-482.
[11] I. Lasiecka and R. Triggiani, Two direct proofs on the
analyticity of the S.C. semigroup arising in abstract thermo-elastic
equations, Advances in Differential Equations 3(3) (1998), 387-416.
DOI: https://doi.org/10.57262/ade/1366399847
[12] I. Lasiecka and R. Triggiani, Analyticity of thermo-elastic
semigroups with coupled hinged/Neumann B.C., Abstract and Applied
Analysis 3 (1998); Article ID 428531.
DOI: https://doi.org/10.1155/S1085337598000487
[13] I. Lasiecka and R. Triggiani, Structural decomposition of
thermo-elastic semigroups with rotational forces, Semigroup Forum
60(1) (2000), 16-66.
DOI: https://doi.org/10.1007/s002330010003
[14] K. S. Liu and Z. Y. Liu, Exponential stability and analyticity of
abstract linear thermoelastic systems, Zeitschrift für angewandte
Mathematik und Physik 48(6) (1997) 885-904.
DOI: https://doi.org/10.1007/s000330050071
[15] Z. Liu and M. Renardy, A note on the equations of a thermoelastic
plate, Applied Mathematics Letters 8(3) (1995), 1-6.
DOI: https://doi.org/10.1016/0893-9659(95)00020-Q
[16] Z. Y. Liu and S. M. Zheng, Exponential stability of the Kirchhoff
plate with thermal or viscoelastic damping, Quarterly of Applied
Mathematics 55(3) (1997), 551-564.
DOI: https://doi.org/10.1090/qam/1466148
[17] Z. Liu and S. Zheng, Semigroups Associated with Dissipative
Systems, Chapman & Hall CRC Research Notes in Mathematics, Boca Raton,
FL, 398 (1999).
[18] S. Nafiri, Uniform polynomial decay and approximation in control
of a family of abstract thermoelastic models, Journal of Dynamical and
Control Systems 29(1) (2021), 209-227.
DOI: https://doi.org/10.1007/s10883-021-09568-9
[19] A. Pazy, Semigroups of Linear Operators and Applications to
Partial Differential Equations, Applied Mathematical Sciences 44,
Springer, 1983.
[20] J. E. M. Rivera, Energy decay rates in linear thermoelasticity,
Funkcialaj Ekvacioj 35(1) (1992), 19-30.
[21] H. D. F. Sare, Z. Liu and R. Racke, Stability of abstract
thermoelastic systems with inertial terms, Journal of Differential
Equations 267(12) (2019), 7085-7134.
DOI: https://doi.org/10.1016/j.jde.2019.07.015
[22] S. W. Taylor, Gevrey Regularity of Solutions of Evolution
Equations and Boundary Controllability, Thesis (Ph.D.) University of
Minnesota, (1989), 182 pp.
[23] L. Tebon, Stabilization of some coupled hyperbolic/parabolic
equations, Discrete and Continuous Dynamical Systems Series B 14(4)
(2010), 1601-1620.
DOI: https://doi.org/10.3934/dcdsb.2010.14.1601
[24] L. Tebou, Uniform analyticity and exponential decay of the
semigroup associated with a thermoelastic plate equation with
perturbed boundary conditions, Comptes Rendus Mathematique 351(13-14)
(2013), 539-544.
DOI: https://doi.org/10.1016/j.crma.2013.07.014
[25] L. Tebou, Regularity and stability for a plate model involving
fractional rotational forces and damping, Zeitschrift für
Angewandte Mathematik und Physik 72(4) (2021); Article 158.
DOI: https://doi.org/10.1007/s00033-021-01589-5