Global existence of solutions for the thermoelastic
Bresse system
Pages: 1395  1406,
Issue 4,
July
2014
doi:10.3934/cpaa.2014.13.1395 Abstract
References
Full text (367.4K)
Related Articles
Yuming Qin  Department of Applied Mathematics, Donghua University, Shanghai 201620, China (email)
Xinguang Yang  College of Information Science and Technology, Donghua University, Shanghai 201620, China (email)
Zhiyong Ma  College of Science, Shanghai Second Polytechnic University, Shanghai, 201209, China (email)
1 
J. A. C. Bresse, Cours de Méchanique Appliquée, Mallet Bachelier, 1859. 

2 
C. M. Dafermos, On the existence and the asymptotic stability of solution to the equations of linear thermoelasticity, Arch. Rational Mech. Anal., 29 (1968), 247271. 

3 
C. M. Dafermos, Asymptotic stability in viscoelascity, Arch. Rational Mech. Anal., 37 (1970), 297308. 

4 
C. M. Dafermos, An abstract Volterra equation with applications to linear viscoelascity, J. Differential Equations, 7 (1990), 554569. 

5 
R. H. Fabiano and K. Ito, Semigroup theory and numerical approximation for equations arising in linear viscoelascity, SIAM J. Math. Anal., 21 (1990), 374393. 

6 
L. H. Fatori and J. E. Muñoz Rivera, Rates of decay to weak thermoelastic Bresse system, IMA J. Appl. Math., 75 (2010), 881904. 

7 
S. W. Hansen, Exponential energy decay in a linear thermoelastic rod, J. Math. Anal. Appl., 167 (1992), 429442. 

8 
F. L. Huang, Characteristic conditions for exponential stability of linear dynamical systems in Hilbert spaces, Ann. Differential Equations, 1 (1985), 4356. 

9 
K. Liu and Z. Liu, On the type of $C_0$semigroup associated with the abstract linear viscoelastic system, Z. angew. Math. Phys., 47 (1996), 115. 

10 
W. J. Liu, Partial exact controllability and exponential stability in higher dimensional linear thermoelascity, ESAIM: Control Optim. Calc. Var., 3 (1998), 2348. 

11 
W. J. Liu, The exponential stabilization of higherdimensional linear system of thermoviscoelasticity, J. Math. Pures Appl., 77 (1998), 355386. 

12 
Z. Liu and B. Rao, Energy decay rate of the thermoelastic Bresse system, Z. angew. Math. Phys., 60 (2009), 5469. 

13 
Z. Liu and S. Zheng, On the exponential stability of linear viscoelasticity and thermoviscoelasticity, Quart. Appl. Math., LIV (1996), 2131. 

14 
Z. Liu and S. Zheng, Semigroups Associated with Dissipative Systems, Research Notes in Mathematics, 389, Chapman & Hall/CRC, Boca Raton, FL, 1999. 

15 
Z. Ma, Exponential stability and global attractors for a thermoelastic Bresse system, Adv. Difference Equations, 1 (2010), 117. 

16 
S. A. Messaoudi and B. SaidHouari, Energy decay in a Timoshenkotype system of thermoelasticity of type III, J. Math. Anal. Appl., 348 (2008), 298307. 

17 
J. E. Muñoz Rivera and H. D. Fernández Sare, Stability of Timoshenko systems with past history, J. Math. Anal. Appl., 339 (2008), 482502. 

18 
A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, SpringerVerlag, New York, Berlin, Heidelbery, Tokyo, 1983. 

19 
J. Prüss, On the spectrum of $C_0$semigroups, Trans. Amer. Math. Soc., 284 (1984), 847857. 

20 
Y. Qin and Z. Ma, Global existence of the higherdimensional linear system of thermoviscoelasticity, Preprint. 

21 
Y. Qin, Nonlinear ParabolicHyperbolic Coupled Systems and Their Attractors, Operator Theory, Advances and Applications, Vol. 184, Birkh\"auser, BaselBostonBerlin. 

22 
Y. Qin, Universal attractor in $H^4$ for the nonlinear onedimensional compressible Navier Stokes equations, J. Differential Equations, 207 (2004), 2172. 

23 
Y. Qin and J. E. Muñoz Rivera, Universal attractors for a nonlinear onedimensional heatconductive viscous real gas, Proc. Roy. Soc. Edinburgh, 132(A) (2002), 685709. 

24 
Y. Qin, S. Deng and B. W. Schulze, Uniform compact attractors for a nonlinear nonautonomous equation of viscoelastisity, J. Partial Differential Equations, 22 (2009), 152192. 

25 
R. Racke, Y. Shibata and S. Zheng, Global solvability and exponential stability in onedimensional nonlinear thermoelasticity, Quart. Appl. Math., 4 (1993), 751763. 

26 
R. Racke and J. E. Muñoz Rivera, Midly dissipative nonlinear Tymoshenko systemsGlobal existence and exponential stability, J. Math. Appl. Anal., 276 (2002), 248278. 

27 
Y. Shibata, Neumann problem for onedimensional nonlinear thermoelascity, Banach Center Publication, 27 (1992), 457480. 

28 
M. Slemrod, Global existence, uniqueness, and asymptotic stability of classical smooth solutions in onedimensional nonlinear thermoelascity, Arch. Rational Mech. Anal., 76 (1981), 97133. 

29 
S. P. Timoshenko, On the correction for shear of the differential equation for transverse vibrations of prismatic bars, Philosophical Magazine, 6 (1921), 744746. 

30 
X. Zhang and E. Zuazua, Decay of solutions of the system of thermoelasticity of type III, Comm. Contemp. Math., 5 (2003), 2583. 

31 
S. Zheng, Nonlinear Evolution Equations, Pitman Monogr. Survey. Pure Appl. Math., Vol. 133, CRC Press, USA, 2004. 

32 
S. Zheng and Y. Qin, Maximal attractor for the system of onedimensional polytropic viscous ideal gas, Quart. Appl. Math., 3 (2001), 579599. 

33 
S. Zheng and Y. Qin, Universal attractors for the NavierStokes equations of compressible and heat conductive fluids in bounded annular domains in $R^n$, Arch. Rational Mech. Anal., 160 (2001), 153179. 

Go to top
