References
- Dafermos CM. On the existence and the asymptotic stability of solution to the equations of linear thermoelasticity. Arch Rational Mech Anal. 1968;29:241–271.
- Muñoz JE. Rivera. Asymptotic behaviour in inhomogeneous linear thermoelasticity, Appl Anal. 1994;53:55–66.
- Racke R. Initial boundary value problems in one-dimensional nonlinear thermoelasticity. Math Methods Appl Sci. 1988;10:517–529.
- Casas PS, Quintanilla R. Exponential decay in one-dimensional porous-thermo-elasticity. Mech Res Commun. 2005;32:652–658.
- Ignaczak J, Ostoja-Starzewski M. Thermoelasticity with finite wave speeds. Oxford mathematical monographs. New York (NY): Oxford University Press; 2009.
- Green AE, Naghdi PM. A re-examination of the basic postulates of thermomechanics. Proc R Soc Lond Ser A. 1991;432:171–194.
- Green AE, Naghdi PM. Thermoelasticity without energy dissipation. J Elast. 1993;31:189–208.
- Green AE, Naghdi PM. On undamped heat waves in an elastic solid. J Therm Stresses. 1992;15:253–264.
- Green AE, Naghdi PM. A unified pocedure for contruction of theories of deformable media, I. Clasical continuum physics. Proc R Soc Lond Ser A. 1995;448:335–356.
- Messaoudi SA, Said-Houari B. Energy decay in a Timoshenko-type system of thermoelasticity of type III. J Math Anal Appl. 2008;348:298–307.
- Messaoudi SA, Fareh A. Energy decay in a Timoshenko-type system of thermoelasticity of type III with different wave-propagation speeds. Arabian J Math. 2013;2:199–207.
- Zhang X, Zuazua E. Decay of solutions of the system of thermoelasticity of type III. Commun Contemp Math. 2003;5:1–59.
- Liu ZY, Quintanilla R. Energy decay rate of a mixed type II and type III thermoelastic system. Discrete Continuous Dyn Syst Ser B. 2010;14:1433–1444.
- Leseduarte MC, Magana A, Quintanilla R. On the time decay of solutions in porous-thermo-elasticity of type II. Discrete Continuous Dyn Syst Ser B. 2010;13:375–391.
- Lazzari B, Nibbi R. On the exponential decay in thermoelasticity without energy dissipation and of type III in presence of an absorbing boundary. J Math Anal Appl. 2008;338:317–329.
- Aouadi M, Lazzari B, Nibbi R. Exponential decay in thermoelastic materials with voids and dissipative boundary without thermal dissipation. Z Angew Math Phys. 2012;63:961–973.
- Fernandez JR, Masida M. Analysis of a problem arising in porous thermoelasticity of type II. J Therm Stresses. 2016;39:513–531.
- Han ZJ, Xu GQ, Tang XQ. Stability analysis of a thermo-elastic system of type II with boundary viscoelastic damping. Z Angew Math Phys. 2012;63:675–689.
- Wang L, Han ZJ, Xu GQ. Exponential stability of serially connected thermoelastic system of type II with nodal damping. Appl Anal. 2014;93:1495–1514.
- Wang L, Han ZJ, Xu GQ. Exponential-stability and super-stability of a thermoelastic system of type II with boundary damping. Discrete Continuous Dyn Syst Ser B. 2015;20:2733–2750.
- Fernández Sare HD, Muñoz Rivera JE. Optimal rates of decay in 2-d thermoelasticity with second sound. J Math Phys. 2012;53:073509. doi:10.1063/1.4734239.
- Lasiecka I, Wilke M. Maximal regularity and global existence of solutions to a quasilinear thermoelastic plate system. Discrete Continuous Dyn Sys. 2013;33:5189–5202.
- Messaoudi SA, Said-Houari B. Energy decay in a Timoshenko-type system with history in thermoelasticity of type III. Adv Differ Equ. 2009;4:375–400.
- Racke R, Jiang S. Evolution equations in thermoelasticity. Boca Raton: Chapman and Hall/CRC; 2000.
- Quintanilla R. Instability and non-existence in the nonlinear theory of thermoelasticity without energy dissipation. Continuum Mech Thermodyn. 2001;13:121–129.
- Djebabla A, Tatar N. Exponential stabilization of the Timoshenko system by a thermo-viscoelastic damping. J Dyn Control Syst. 2010;16:189–210.
- Wang JM, Guo BZ. On dynamic behavior of a hyperbolic system derived from a thermoelastic equation with memory type. J Franklin Inst. 2007;344:75–96.
- Pisano A, Orlov Y, Usai E. Tracking control of the uncertain heat and wave equation via power-fractional and sliding-mode techniques. SIAM J Control Optim. 2011;49:363–382.
- Yang KJ, Hong KS, Matsuno F. Energy-based control of axially translating beams: varying tension, varying speed, and disturbance adaptation. IEEE Trans Control Syst Technol. 2005;13:1045–1054.
- Chauvin J. Observer design for a class of wave equation driven by an unknown periodic input. Proceedings of 18th IFAC World Congress. Milan: Elsevier; 2011. p. 1332–1337.
- Guo W, Guo BZ. Parameter estimation and non-collocated adaptive stabilization for a wave equation subject to general boundary harmonic disturbance. IEEE Trans Autom Control. 2013;58:1631–1642.
- Guo W, Guo BZ, Shao ZC. Parameter estimation and stabilization for a wave equation with boundary output harmonic disturbance and non-collocated control. Int J Robust Nonlinear Control. 2011;21:1297–1321.
- Cheng MB, Radisavljevic V, Su WC. Output-feedback boundary control of an uncertain heat equation with noncollocated observation: a sliding-mode approach. Proceedings 5th IEEE Conference on Industrial Electronics and Applications. Taichung: Institute of Electrical and Electronics Engineers (IEEE); 2010. p. 2187–2192.
- Cheng MB, Radisavljevic V, Su WC. Sliding mode boundary control of a parabolic PDE system with parameter variations and boundary uncertainties. Automatica. 2001;47:381–387.
- Tang SX, Krstic M. Sliding mode control to the stabilization of a linear 2 × 2 hyperbolic system with boundary input disturbance. Proceedings of the 2014 American Control Conference. Portland; Institute of Electrical and Electronics Engineers (IEEE); 2014. p. 1027–1032.
- Ge SS, Zhang S, He W. Vibration control of an Euler-Bernoulli beam under unknown spatiotemporally varying disturbance. Int J Control. 2011;84:947–960.
- He W, Ge SS. Robust adaptive boundary control of a vibrating string under unknown time-varying disturbance. IEEE Trans Control Syst Technol. 2012;20:48–58.
- Han JQ. From PID to active disturbance rejection control. IEEE Trans Ind Electron. 2009;56:900–906.
- Gao Z. Active disturbance rejection control: aparadigm shift in feedback control system design. Proceedings of the 2006 American Control Conference. Minneapolis: Institute of Electrical and Electronics Engineers (IEEE); 2006. p. 2399–2405.
- Guo BZ, Jin FF. The active disturbance rejection and sliding mode control approach to the stabilization of the Euler-Bernoulli beam equation with boundary input disturbance. Automatica. 2013;49:2911–2918.
- Guo BZ, Jin FF. Sliding mode and active disturbance rejection control to stabilization of one-dimensional anti-stable wave equations subject to disturbance in boundary input. IEEE Trans Autom Control. 2013;58:1269–1274.
- Liu JJ, Wang JM. Active disturbance rejection control and sliding mode control of one dimensional unstable heat equation with boundary uncertainties. IMA J Math Control Inf. 2015;32:97–117.
- Pazy A. Semigroups of linear operators and applications to partial differential equations. Berlin: Springer-Verlag; 1983.
- Trefethen LN. Spectral methods in Matlab. Philadelphia (PA): SIAM; 2000.