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On the threshold for Kato's selfadjointness problem and its $L^p$-generalization
The effect of the wave speeds and the frictional damping terms on the decay rate of the Bresse system
1. | ALHOSN University, Mathematics and Natural Sciences Department, PO Box 38772, Abu Dhabi, United Arab Emirates, United Arab Emirates |
References:
[1] |
F. Alabau Boussouira, J. E. Muñoz Rivera and D. S. Almeida Júnior, Stability to weak dissipative Bresse system, J. Math. Anal. Appl., 374 (2011), 481-498.
doi: 10.1016/j.jmaa.2010.07.046. |
[2] |
M. M. Cavalcanti, V. N Domingos Cavalcanti, F. A Falcão Nascimento, I Lasiecka and J. H Rodrigues, Uniform decay rates for the energy of Timoshenko system with the arbitrary speeds of propagation and localized nonlinear damping, Z. Angew. Math. Phys., (2013), 1-18.
doi: 10.1007/s00033-013-0380-7. |
[3] |
L. H. Fatori and R. N. Monteiro, The optimal decay rate for a weak dissipative Bresse system, Appl. Math. Lett., 25 (2012), 600-604.
doi: 10.1016/j.aml.2011.09.067. |
[4] |
L. H. Fatori and J. E. Muñoz Rivera, Rates of decay to weak thermoelastic Bresse system, IMA Journal of Applied Mathematics, 75 (2010), 881-904.
doi: 10.1093/imamat/hxq038. |
[5] |
M. Grobbelaar-Van Dalsen, Polynomial decay rate of a thermoelastic mindlin-Timoshenko plate model with dirichlet boundary conditions, Z. Angew. Math. Phys., (2013), 1-16.
doi: 10.1007/s00033-013-0391-4. |
[6] |
K. Ide, K. Haramoto and S. Kawashima, Decay property of regularity-loss type for dissipative Timoshenko system, Math. Mod. Meth. Appl. Sci., 18 (2008), 647-667.
doi: 10.1142/S0218202508002802. |
[7] |
K. Ide and S. Kawashima, Decay property of regularity-loss type and nonlinear effects for dissipative Timoshenko system, Math. Mod. Meth. Appl. Sci., 18 (2008), 1001-1025.
doi: 10.1142/S0218202508002930. |
[8] |
Z. Liu and B. Rao, Energy decay rate of the thermoelastic Bresse system, Z. Angew. Math. Phys., 60 (2009), 54-69.
doi: 10.1007/s00033-008-6122-6. |
[9] |
A. Matsumura, On the asymptotic behavior of solutions of semi-linear wave equations, Publ. Res. Inst. Math. Sci. Kyoto. Univ, 12 (1976), 169-189.
doi: 10.2977/prims/1195190962. |
[10] |
L. Nirenberg, On elliptic partial differential equations, Ann. Scuola Norm. Sup. Pisa, 13 (1959), 115-162. |
[11] |
N. Noun and A. Wehbe, Stabilisation faible interne locale de système élastique de Bresse, C. R. Math. Acad. Sci. Paris, 350 (2012), 493-498.
doi: 10.1016/j.crma.2012.04.003. |
[12] |
R. Racke and B. Said-Houari, Decay rates and global existence for semilinear dissipative Timoshenko systems, Quart. Appl. Math., 71 (2013), 229-266.
doi: 10.1090/S0033-569X-2012-01280-8. |
[13] |
C. A. Raposo, J. Ferreira, M. L. Santos and N. N. O. Castro, Exponential stability for the Timoshenko system with two weak dampings, Appl. Math. Letters, 18 (2005), 535-541.
doi: 10.1016/j.aml.2004.03.017. |
[14] |
M. L. Santos, A. Soufyane and D. S. A. Júnior, Asymptotic behavior to bresse system with past history, Quarterly of Applied Mathematics, Accepted, 2013. |
[15] |
J. A. Soriano, J. E. Muñoz Rivera and L. H. Fatori, Bresse system with indefinite damping, J. Math. Anal. Appl., 387 (2012), 284-290.
doi: 10.1016/j.jmaa.2011.08.072. |
show all references
References:
[1] |
F. Alabau Boussouira, J. E. Muñoz Rivera and D. S. Almeida Júnior, Stability to weak dissipative Bresse system, J. Math. Anal. Appl., 374 (2011), 481-498.
doi: 10.1016/j.jmaa.2010.07.046. |
[2] |
M. M. Cavalcanti, V. N Domingos Cavalcanti, F. A Falcão Nascimento, I Lasiecka and J. H Rodrigues, Uniform decay rates for the energy of Timoshenko system with the arbitrary speeds of propagation and localized nonlinear damping, Z. Angew. Math. Phys., (2013), 1-18.
doi: 10.1007/s00033-013-0380-7. |
[3] |
L. H. Fatori and R. N. Monteiro, The optimal decay rate for a weak dissipative Bresse system, Appl. Math. Lett., 25 (2012), 600-604.
doi: 10.1016/j.aml.2011.09.067. |
[4] |
L. H. Fatori and J. E. Muñoz Rivera, Rates of decay to weak thermoelastic Bresse system, IMA Journal of Applied Mathematics, 75 (2010), 881-904.
doi: 10.1093/imamat/hxq038. |
[5] |
M. Grobbelaar-Van Dalsen, Polynomial decay rate of a thermoelastic mindlin-Timoshenko plate model with dirichlet boundary conditions, Z. Angew. Math. Phys., (2013), 1-16.
doi: 10.1007/s00033-013-0391-4. |
[6] |
K. Ide, K. Haramoto and S. Kawashima, Decay property of regularity-loss type for dissipative Timoshenko system, Math. Mod. Meth. Appl. Sci., 18 (2008), 647-667.
doi: 10.1142/S0218202508002802. |
[7] |
K. Ide and S. Kawashima, Decay property of regularity-loss type and nonlinear effects for dissipative Timoshenko system, Math. Mod. Meth. Appl. Sci., 18 (2008), 1001-1025.
doi: 10.1142/S0218202508002930. |
[8] |
Z. Liu and B. Rao, Energy decay rate of the thermoelastic Bresse system, Z. Angew. Math. Phys., 60 (2009), 54-69.
doi: 10.1007/s00033-008-6122-6. |
[9] |
A. Matsumura, On the asymptotic behavior of solutions of semi-linear wave equations, Publ. Res. Inst. Math. Sci. Kyoto. Univ, 12 (1976), 169-189.
doi: 10.2977/prims/1195190962. |
[10] |
L. Nirenberg, On elliptic partial differential equations, Ann. Scuola Norm. Sup. Pisa, 13 (1959), 115-162. |
[11] |
N. Noun and A. Wehbe, Stabilisation faible interne locale de système élastique de Bresse, C. R. Math. Acad. Sci. Paris, 350 (2012), 493-498.
doi: 10.1016/j.crma.2012.04.003. |
[12] |
R. Racke and B. Said-Houari, Decay rates and global existence for semilinear dissipative Timoshenko systems, Quart. Appl. Math., 71 (2013), 229-266.
doi: 10.1090/S0033-569X-2012-01280-8. |
[13] |
C. A. Raposo, J. Ferreira, M. L. Santos and N. N. O. Castro, Exponential stability for the Timoshenko system with two weak dampings, Appl. Math. Letters, 18 (2005), 535-541.
doi: 10.1016/j.aml.2004.03.017. |
[14] |
M. L. Santos, A. Soufyane and D. S. A. Júnior, Asymptotic behavior to bresse system with past history, Quarterly of Applied Mathematics, Accepted, 2013. |
[15] |
J. A. Soriano, J. E. Muñoz Rivera and L. H. Fatori, Bresse system with indefinite damping, J. Math. Anal. Appl., 387 (2012), 284-290.
doi: 10.1016/j.jmaa.2011.08.072. |
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