-
Previous Article
Uniform controllability of semidiscrete approximations for parabolic systems in Banach spaces
- DCDS-B Home
- This Issue
-
Next Article
Concentration phenomenon in a nonlocal equation modeling phytoplankton growth
Exponential decay for linear damped porous thermoelastic systems with second sound
1. | King Fahd University of Petroleum and Minerals, Department of Mathematics and Statistics, Dhahran 31261 |
2. | Laboratoire de thèorie des operateurs et EDP: fondements et applications, Faculté des Sciences et de technologie, Universit, El Oued 39000, Algeria |
References:
[1] |
P. S. Casas and R. Quintanilla, Exponential decay in one-dimensional porous thermoelasticity, Mech. Res. Comm., 32 (2005), 652-658.
doi: 10.1016/j.mechrescom.2005.02.015. |
[2] |
H. D. Fernàndez-Sare and R. Racke, On the stability of damped Timoshenko system Cattaneo versus Fourier law$^*$, Arch. Rat. Mech. Anal., 194 (2009), 221-251.
doi: 10.1007/s00205-009-0220-2. |
[3] |
A. Guesmia, S. A. Messaoudi and A. Wehbe, Uniform decay in mildly damped Timoshenko system with non-equal wave speed propagation, Dynamic Systems and Applications, 21 (2012), 133-146. |
[4] |
S. W. Hansen, Exponential energy decay in a linear thermoelastic rod, J. Math. Anal. appl., 167 (1992), 429-442.
doi: 10.1016/0022-247X(92)90217-2. |
[5] |
Z. J. Han and G. Q. Xu, Exponential decay result in non-uniform porous-thermo-elasticity model of Lord-Shulman type, Disc. Cont. Dyn. Sys. B, 17 (2012), 57-77.
doi: 10.3934/dcdsb.2012.17.57. |
[6] |
H. W. Lord and Y. Shulman, A generalized dynamical theory of thermoelasticity, J. Mech. Phys. Sol., 15 (1967), 299-309.
doi: 10.1016/0022-5096(67)90024-5. |
[7] |
A. Magaña and R. Quintanilla, On the time decay of solutions in one-dimensional theories of porous materials, Internat. J. Solids Struct., 43 (2006), 3414-3427.
doi: 10.1016/j.ijsolstr.2005.06.077. |
[8] |
S. A. Messaoudi and A. Fareh, General decay for a porous thermoelastic system with memory: The case of equal speeds, Nonlinear analysis: TMA, 74 (2011), 6895-6906.
doi: 10.1016/j.na.2011.07.012. |
[9] |
S. A. Messaoudi and A. Fareh, General decay for a porous thermoelastic system with memory: The case of nonequal speeds, Acta Mathimatica Scientia, 33 (2013), 23-40.
doi: 10.1016/S0252-9602(12)60192-1. |
[10] |
S. A. Messaoudi, M. Pokojovy and B. Said-Houari, Nonlinear damped Timoshenko system with second sound - Global existence and exponential stability, Math. Meth. Appl. Sci., 32 (2009), 505-534.
doi: 10.1002/mma.1049. |
[11] |
J. E. Muñoz Rivera, Energy decay rate in linear thermoelasticity, Funkcial Ekvac., 35 (1992), 19-30. |
[12] |
J. E. Muñoz Rivera and R. Racke, Mildly dissipative nonlinear Timoshenko systems - global existence and exponential stability, J. Math. Anal. Appl., 276 (2002), 248-278.
doi: 10.1016/S0022-247X(02)00436-5. |
[13] |
J. E. Muñoz Rivera and R. Quintanilla, On the time polynomial decay in elastic solids with voids, J. Math. Anal. Appl., 338 (2008), 1296-1309.
doi: 10.1016/j.jmaa.2007.06.005. |
[14] |
R. Quintanilla, Slow decay in one-dimensional porous dissipation elasticity, Applied Math. Letters, 16 (2003), 487-491.
doi: 10.1016/S0893-9659(03)00025-9. |
[15] |
R. Racke, Thermoelasticity with second sound, exponential stability in linear and non linear 1-d, Math. Meth. Appl. Sci., 25 (2002), 409-441.
doi: 10.1002/mma.298. |
[16] |
R. Racke, Asymptotic behavior of solutions in linear 2- or 3-D thermoelasticity with second sound, Quart. Appl. Math., 61 (2003), 315-328. |
[17] |
M. L. Santos, D. S. Almeida Júnior and J. E. Muñoz Rivera, The stability number of the Timoshenko system with second sound, J. Diff. Eqns., 253 (2012), 2715-2733.
doi: 10.1016/j.jde.2012.07.012. |
[18] |
A. Soufyane, Energy decay for porous-thermo-elasticity systems of memory type, Appl. Anal., 87 (2008), 451-464.
doi: 10.1080/00036810802035634. |
[19] |
M. A. Tarabek, On the existence of smooth solutions in one-dimensional nonlinear thermoelasticity with second sound, Quarterly of Applied Mathematics, 50 (1992), 727-742. |
show all references
References:
[1] |
P. S. Casas and R. Quintanilla, Exponential decay in one-dimensional porous thermoelasticity, Mech. Res. Comm., 32 (2005), 652-658.
doi: 10.1016/j.mechrescom.2005.02.015. |
[2] |
H. D. Fernàndez-Sare and R. Racke, On the stability of damped Timoshenko system Cattaneo versus Fourier law$^*$, Arch. Rat. Mech. Anal., 194 (2009), 221-251.
doi: 10.1007/s00205-009-0220-2. |
[3] |
A. Guesmia, S. A. Messaoudi and A. Wehbe, Uniform decay in mildly damped Timoshenko system with non-equal wave speed propagation, Dynamic Systems and Applications, 21 (2012), 133-146. |
[4] |
S. W. Hansen, Exponential energy decay in a linear thermoelastic rod, J. Math. Anal. appl., 167 (1992), 429-442.
doi: 10.1016/0022-247X(92)90217-2. |
[5] |
Z. J. Han and G. Q. Xu, Exponential decay result in non-uniform porous-thermo-elasticity model of Lord-Shulman type, Disc. Cont. Dyn. Sys. B, 17 (2012), 57-77.
doi: 10.3934/dcdsb.2012.17.57. |
[6] |
H. W. Lord and Y. Shulman, A generalized dynamical theory of thermoelasticity, J. Mech. Phys. Sol., 15 (1967), 299-309.
doi: 10.1016/0022-5096(67)90024-5. |
[7] |
A. Magaña and R. Quintanilla, On the time decay of solutions in one-dimensional theories of porous materials, Internat. J. Solids Struct., 43 (2006), 3414-3427.
doi: 10.1016/j.ijsolstr.2005.06.077. |
[8] |
S. A. Messaoudi and A. Fareh, General decay for a porous thermoelastic system with memory: The case of equal speeds, Nonlinear analysis: TMA, 74 (2011), 6895-6906.
doi: 10.1016/j.na.2011.07.012. |
[9] |
S. A. Messaoudi and A. Fareh, General decay for a porous thermoelastic system with memory: The case of nonequal speeds, Acta Mathimatica Scientia, 33 (2013), 23-40.
doi: 10.1016/S0252-9602(12)60192-1. |
[10] |
S. A. Messaoudi, M. Pokojovy and B. Said-Houari, Nonlinear damped Timoshenko system with second sound - Global existence and exponential stability, Math. Meth. Appl. Sci., 32 (2009), 505-534.
doi: 10.1002/mma.1049. |
[11] |
J. E. Muñoz Rivera, Energy decay rate in linear thermoelasticity, Funkcial Ekvac., 35 (1992), 19-30. |
[12] |
J. E. Muñoz Rivera and R. Racke, Mildly dissipative nonlinear Timoshenko systems - global existence and exponential stability, J. Math. Anal. Appl., 276 (2002), 248-278.
doi: 10.1016/S0022-247X(02)00436-5. |
[13] |
J. E. Muñoz Rivera and R. Quintanilla, On the time polynomial decay in elastic solids with voids, J. Math. Anal. Appl., 338 (2008), 1296-1309.
doi: 10.1016/j.jmaa.2007.06.005. |
[14] |
R. Quintanilla, Slow decay in one-dimensional porous dissipation elasticity, Applied Math. Letters, 16 (2003), 487-491.
doi: 10.1016/S0893-9659(03)00025-9. |
[15] |
R. Racke, Thermoelasticity with second sound, exponential stability in linear and non linear 1-d, Math. Meth. Appl. Sci., 25 (2002), 409-441.
doi: 10.1002/mma.298. |
[16] |
R. Racke, Asymptotic behavior of solutions in linear 2- or 3-D thermoelasticity with second sound, Quart. Appl. Math., 61 (2003), 315-328. |
[17] |
M. L. Santos, D. S. Almeida Júnior and J. E. Muñoz Rivera, The stability number of the Timoshenko system with second sound, J. Diff. Eqns., 253 (2012), 2715-2733.
doi: 10.1016/j.jde.2012.07.012. |
[18] |
A. Soufyane, Energy decay for porous-thermo-elasticity systems of memory type, Appl. Anal., 87 (2008), 451-464.
doi: 10.1080/00036810802035634. |
[19] |
M. A. Tarabek, On the existence of smooth solutions in one-dimensional nonlinear thermoelasticity with second sound, Quarterly of Applied Mathematics, 50 (1992), 727-742. |
[1] |
Salah Drabla, Salim A. Messaoudi, Fairouz Boulanouar. A general decay result for a multi-dimensional weakly damped thermoelastic system with second sound. Discrete and Continuous Dynamical Systems - B, 2017, 22 (4) : 1329-1339. doi: 10.3934/dcdsb.2017064 |
[2] |
Edriss S. Titi, Saber Trabelsi. Global well-posedness of a 3D MHD model in porous media. Journal of Geometric Mechanics, 2019, 11 (4) : 621-637. doi: 10.3934/jgm.2019031 |
[3] |
Ramón Quintanilla, Reinhard Racke. Stability for thermoelastic plates with two temperatures. Discrete and Continuous Dynamical Systems, 2017, 37 (12) : 6333-6352. doi: 10.3934/dcds.2017274 |
[4] |
Ivan C. Christov. On a C-integrable equation for second sound propagation in heated dielectrics. Evolution Equations and Control Theory, 2019, 8 (1) : 57-72. doi: 10.3934/eect.2019004 |
[5] |
Pedro M. Jordan. Second-sound phenomena in inviscid, thermally relaxing gases. Discrete and Continuous Dynamical Systems - B, 2014, 19 (7) : 2189-2205. doi: 10.3934/dcdsb.2014.19.2189 |
[6] |
Yuxi Hu, Na Wang. On global solutions in one-dimensional thermoelasticity with second sound in the half line. Communications on Pure and Applied Analysis, 2015, 14 (5) : 1671-1683. doi: 10.3934/cpaa.2015.14.1671 |
[7] |
Makram Hamouda, Ahmed Bchatnia, Mohamed Ali Ayadi. Numerical solutions for a Timoshenko-type system with thermoelasticity with second sound. Discrete and Continuous Dynamical Systems - S, 2021, 14 (8) : 2975-2992. doi: 10.3934/dcdss.2021001 |
[8] |
Wenming Hu, Huicheng Yin. Well-posedness of low regularity solutions to the second order strictly hyperbolic equations with non-Lipschitzian coefficients. Communications on Pure and Applied Analysis, 2019, 18 (4) : 1891-1919. doi: 10.3934/cpaa.2019088 |
[9] |
Giorgio Menegatti, Luca Rondi. Stability for the acoustic scattering problem for sound-hard scatterers. Inverse Problems and Imaging, 2013, 7 (4) : 1307-1329. doi: 10.3934/ipi.2013.7.1307 |
[10] |
Ugur G. Abdulla. On the optimal control of the free boundary problems for the second order parabolic equations. I. Well-posedness and convergence of the method of lines. Inverse Problems and Imaging, 2013, 7 (2) : 307-340. doi: 10.3934/ipi.2013.7.307 |
[11] |
K. Domelevo. Well-posedness of a kinetic model of dispersed two-phase flow with point-particles and stability of travelling waves. Discrete and Continuous Dynamical Systems - B, 2002, 2 (4) : 591-607. doi: 10.3934/dcdsb.2002.2.591 |
[12] |
Fujun Zhou, Shangbin Cui. Well-posedness and stability of a multidimensional moving boundary problem modeling the growth of tumor cord. Discrete and Continuous Dynamical Systems, 2008, 21 (3) : 929-943. doi: 10.3934/dcds.2008.21.929 |
[13] |
Joachim Escher, Anca-Voichita Matioc. Well-posedness and stability analysis for a moving boundary problem modelling the growth of nonnecrotic tumors. Discrete and Continuous Dynamical Systems - B, 2011, 15 (3) : 573-596. doi: 10.3934/dcdsb.2011.15.573 |
[14] |
Stefan Meyer, Mathias Wilke. Global well-posedness and exponential stability for Kuznetsov's equation in $L_p$-spaces. Evolution Equations and Control Theory, 2013, 2 (2) : 365-378. doi: 10.3934/eect.2013.2.365 |
[15] |
Ahmed Bchatnia, Aissa Guesmia. Well-posedness and asymptotic stability for the Lamé system with infinite memories in a bounded domain. Mathematical Control and Related Fields, 2014, 4 (4) : 451-463. doi: 10.3934/mcrf.2014.4.451 |
[16] |
Aissa Guesmia, Nasser-eddine Tatar. Some well-posedness and stability results for abstract hyperbolic equations with infinite memory and distributed time delay. Communications on Pure and Applied Analysis, 2015, 14 (2) : 457-491. doi: 10.3934/cpaa.2015.14.457 |
[17] |
Jiang Xu. Well-posedness and stability of classical solutions to the multidimensional full hydrodynamic model for semiconductors. Communications on Pure and Applied Analysis, 2009, 8 (3) : 1073-1092. doi: 10.3934/cpaa.2009.8.1073 |
[18] |
Kelin Li, Huafei Di. On the well-posedness and stability for the fourth-order Schrödinger equation with nonlinear derivative term. Discrete and Continuous Dynamical Systems - S, 2021, 14 (12) : 4293-4320. doi: 10.3934/dcdss.2021122 |
[19] |
Akram Ben Aissa. Well-posedness and direct internal stability of coupled non-degenrate Kirchhoff system via heat conduction. Discrete and Continuous Dynamical Systems - S, 2022, 15 (5) : 983-993. doi: 10.3934/dcdss.2021106 |
[20] |
Baoyan Sun, Kung-Chien Wu. Global well-posedness and exponential stability for the fermion equation in weighted Sobolev spaces. Discrete and Continuous Dynamical Systems - B, 2022, 27 (5) : 2537-2562. doi: 10.3934/dcdsb.2021147 |
2021 Impact Factor: 1.497
Tools
Metrics
Other articles
by authors
[Back to Top]