Optimal decay rates and the selfadjoint property in overdamped systems

Journal of Differential Equations

Volumn 246, Issue 7, 2009, Pages 2813-2828

  Pellicer, M ^a   Sola Morales J ^b  

^a UNIVERSITY OF GIRONA   (Spain)

^b UNIVERSITAT POLITÈCNICA DE CATALUNYA   (Spain)

Author keywords

Optimal decay rate; Overdamping; Selfadjoint operators; Strongly damped wave equations

Indexed keywords

EID: 60349112132     PISSN: 00220396     EISSN: 10902732     Source Type: Journal    
DOI: 10.1016/j.jde.2009.01.010     Document Type: Article

References (23)

1. Bátkai A., Engel K.-J., Prüss J., and Schnaubelt R. Polynomial stability of operator semigroups. Math. Nachr. 279 13-14 (2006) 1425-1440
2. Chen S., and Triggiani R. Proof of extensions of two conjectures on structural damping for elastic systems. Pacific J. Math. 136 1 (1989) 15-55
3. Freitas P. Eigenvalue problems for the wave equation with strong damping. Proc. Roy. Soc. Edinburgh Sect. A 127 4 (1997) 755-771
4. Griffel D.H. Applied Functional Analysis (2002), Dover Publications
5. Kato T. Perturbation Theory for Linear Operator. Classics Math. (1980), Springer-Verlag
6. Lebeau G., and Zuazua E. Decay rates for the three-dimensional linear system of thermoelasticity. Arch. Ration. Mech. Anal. 148 3 (1999) 179-231
7. Littman W., and Liu B. On the spectral properties and stabilization of acoustic flow. SIAM J. Appl. Math. 59 1 (1999) 17-34
8. Liu Z., and Rao B. Characterization of polynomial decay rate for the solution of linear evolution equation. Z. Angew. Math. Phys. 56 4 (2005) 630-644
9. Massatt P. Limiting behaviour for strongly damped nonlinear wave equations. J. Differential Equations 48 (1983) 334-349
10. Pellicer M. Large time dynamics of a nonlinear spring-mass-damper model. Nonlinear Anal. 69 9 (2008) 3110-3127
11. Pellicer M., and Solà-Morales J. Analysis of a viscoelastic spring-mass model. J. Math. Anal. Appl. 294 (2004) 687-698
12. Pellicer M., and Solà-Morales J. Spectral analysis and limit behaviours in a spring-mass system. Commun. Pure Appl. Anal. 7 3 (2008) 563-577
13. Phung K.D. Polynomial decay rate for the dissipative wave equation. J. Differential Equations 240 (2007) 92-124
14. Muñoz Rivera J.E., and Quintanilla R. On the time polynomial decay in elastic solids with voids. J. Math. Anal. Appl. 338 2 (2008) 1296-1309
15. Muñoz Rivera J.E., and Racke R. Polynomial stability in two-dimensional magneto-elasticity. IMA J. Appl. Math. 66 3 (2001) 269-283
16. Rao B., and Wehbe A. Polynomial energy decay rate and strong stability of Kirchhoff plates with non-compact resolvent. J. Evol. Equ. 5 2 (2005) 137-152
17. Rauch J., Zhang X., and Zuazua E. Polynomial decay for a hyperbolic-parabolic coupled system. J. Math. Pures Appl. (9) 84 4 (2005) 407-470
18. Russell D.L. Decay rates for weakly damped systems in Hilbert space obtained with control-theoretic methods. J. Differential Equations 19 2 (1975) 344-370
19. Shubov M.A. Basis property of eigenfunctions of nonselfadjoint operator pencils generated by the equation of nonhomogeneous damped string. Integral Equations Operator Theory 25 3 (1996) 289-328
20. Shubov M.A. Spectral operators generated by damped hyperbolic equations. Integral Equations Operator Theory 28 3 (1997) 358-372
21. Zhang X., and Zuazua E. Unique continuation for the linearized Benjamin-Bona-Mahony equation with space-dependent potential. Math. Ann. 325 3 (2003) 543-582
22. Zhang X., and Zuazua E. Polynomial decay and control of a 1-d model for fluid-structure interaction. C. R. Math. Acad. Sci. Paris 336 9 (2003) 745-750
23. Zhang X., and Zuazua E. Control, observation and polynomial decay for a coupled heat-wave system. C. R. Math. Acad. Sci. Paris 336 10 (2003) 823-828