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On global solutions in one-dimensional thermoelasticity with second sound in the half line
1. | Department of Mathematics, China University of Mining and Technology, Beijing, 100083, China |
2. | Department of Mathematics, Tianjin University of Technology, Tianjin 300384, China |
References:
[1] |
K. Beauchard and E. Zuazua, Large time asymptotics for partially dissipative hyperbolic systems,, \emph{Arch. Ration. Mech. Anal.}, 199 (2011), 177.
doi: 10.1007/s00205-010-0321-y. |
[2] |
C. Benzoni-Gavage and D. Serre, Multi-dimensional Hyperbolic Partial Differential Equations-First-order Systems and Application,, Clarendon Press, (2007).
|
[3] |
S. Bianchini, B. Hanouzet and R. Natalini, Asymptotic behavior of smooth solutions for partially dissipative hyperbolic systems with a convex entropy,, \emph{Comm. Pure Appl. Math.}, 60 (2007), 1559.
doi: 10.1002/cpa.20195. |
[4] |
C. M. Dafermos and L. Hsiao, Development of singularities in solutions of the equations of nonlinear thermoelasticity,, \emph{Quart. Appl. Math.}, 44 (1986), 463.
|
[5] |
H. D. Fernández Sare and R. Racke, On the stability of damped Timoshenko systems-Cattaneo versus Fourier law,, \emph{Arch. Ration. Mech. Anal.}, 194 (2009), 221.
doi: 10.1007/s00205-009-0220-2. |
[6] |
I. Hansen, Lebensdauer von klassischen Lösungen nichtlinearer Thermoelastizitätsgleichungen,, Diploma thesis, (1994). Google Scholar |
[7] |
Y. Hu, Global solvability in thermoelasticity with second sound on the semi-axis,, \emph{J. Part. Diff. Eq.}, 25 (2012), 37.
|
[8] |
Y. Hu and R. Racke, Formation of singularities in one-dimensional thermoelasticity with second sound,, \emph{Quart. Appl. Math.}, 72 (2014), 311.
doi: 10.1090/S0033-569X-2014-01336-2. |
[9] |
T. J. R. Hughes, T. Kato and J. E. Marsden, Well-posed quasi-linear second-order hyperbolic systems with applications to nonlinear elastodynamics and general relaticity,, \emph{Arch. Rational Mech. Anal.}, 63 (1977), 273.
|
[10] |
W. J. Hrusa and S. A. Messaoudi, On formation of singularities in one-dimensional nonlinear thermoelasticity,, \emph{Arch. Ration. Mech. Anal.}, 111 (1990), 135.
doi: 10.1007/BF00375405. |
[11] |
W. J. Hrusa and M. A. Tarabek, On smooth solutions of the Cauchy problem in one-dimensional nonlinear thermoelasticity,, \emph{Quart. Appl. Math.}, 47 (1989), 631.
|
[12] |
S. Jiang, Global existence and asymptotic behavior of smooth solutions in one-dimensional nonlinear thermoelasticity,, \emph{Proc. Roy. Soc. Edinburgh}, 115A (1990), 257.
doi: 10.1017/S0308210500020631. |
[13] |
S. Jiang, Global solutions of the Dirichlet problem in one-dimensional nonlinear thermoelasticity,, \emph{SFB, 138 (1990). Google Scholar |
[14] |
S. Jiang, On global smooth solutions to the one-dimensional equations of nonlnear inhomogeneous thermoelasticity,, \emph{Nonlinear Anal., 20 (1993), 1245.
doi: 10.1016/0362-546X(93)90154-K. |
[15] |
S. Jiang and R. Racke, Evolution Equations in Thermoelasticity,, Chapman and Hall/CRC Monographs and Surveys in Pure and Appl. Math. Vol. 112, (2000).
|
[16] |
A. Kasimov, R. Racke and B. Said-Houari, Global existence and decay properties for solutions of the Cauchy problem in one-dimensional thermoelasticity with second sound,, \emph{Applicable Analysis}, 93 (2014), 911.
doi: 10.1080/00036811.2013.801457. |
[17] |
T.-T, Li, Global Classical Solutions for Quasilinear Hyperbolic Systems,, Masson, (1994).
|
[18] |
S. A. Messaoudi and B. Said-Houari, Exponetial stability in one-dimensional non-linear thermoelasticity with second sound,, \emph{Math. Methods Appl. Sci.}, 28 (2005), 205.
doi: 10.1002/mma.556. |
[19] |
R. Racke and Y. Shibata, Global smooth solutions and asymptotic stability in one-dimensional nonlinear thermoelasticity,, \emph{Arch. Rational Mech. Anal.}, 116 (1991), 1.
doi: 10.1007/BF00375601. |
[20] |
R. Racke and Y. Shibada, Global solvability and exponential stability in one-dimensional nonlinear thermoelasticity,, \emph{Quart. Appl. Math.}, 51 (1993), 751.
|
[21] |
R. Racke, Thermoelasticity with second sound--Exponential stability in linear and non-linear 1-d,, \emph{Math. Meth. Appl. Sci.}, 25 (2002), 409.
doi: 10.1002/mma.298. |
[22] |
R. Racke, Thermoelasticity, Handbook of Differential Equations,, Chapter 4, (2009), 315.
doi: 10.1016/S1874-5717(08)00211-9. |
[23] |
R. Racke and Y. G. Wang, Nonlinear well-posedness and rates of decay in thermoelasticity with second sound,, \emph{J. Hyperbolic Differential Equations}, 5 (2008), 25.
doi: 10.1142/S021989160800143X. |
[24] |
J. E. M. Rivera, Energy decay rates in linear thermoelasticity,, \emph{Funkcial. Ekvac.}, 35 (1992), 19.
|
[25] |
Y. Shizuta and S. Kawashima, Systems of equations of hyperbolic-parabolic type with applications to the discrete Boltzmann equation,, \emph{Hokkaido Math. J.}, 14 (1995), 249.
doi: 10.14492/hokmj/1381757663. |
[26] |
M. A. Tarabek, On the existence of smooth solutions in one-dimensional nonlinear thermoelasticity with second sound,, \emph{Quart. Appl. Math.}, 50 (1992), 727.
|
show all references
References:
[1] |
K. Beauchard and E. Zuazua, Large time asymptotics for partially dissipative hyperbolic systems,, \emph{Arch. Ration. Mech. Anal.}, 199 (2011), 177.
doi: 10.1007/s00205-010-0321-y. |
[2] |
C. Benzoni-Gavage and D. Serre, Multi-dimensional Hyperbolic Partial Differential Equations-First-order Systems and Application,, Clarendon Press, (2007).
|
[3] |
S. Bianchini, B. Hanouzet and R. Natalini, Asymptotic behavior of smooth solutions for partially dissipative hyperbolic systems with a convex entropy,, \emph{Comm. Pure Appl. Math.}, 60 (2007), 1559.
doi: 10.1002/cpa.20195. |
[4] |
C. M. Dafermos and L. Hsiao, Development of singularities in solutions of the equations of nonlinear thermoelasticity,, \emph{Quart. Appl. Math.}, 44 (1986), 463.
|
[5] |
H. D. Fernández Sare and R. Racke, On the stability of damped Timoshenko systems-Cattaneo versus Fourier law,, \emph{Arch. Ration. Mech. Anal.}, 194 (2009), 221.
doi: 10.1007/s00205-009-0220-2. |
[6] |
I. Hansen, Lebensdauer von klassischen Lösungen nichtlinearer Thermoelastizitätsgleichungen,, Diploma thesis, (1994). Google Scholar |
[7] |
Y. Hu, Global solvability in thermoelasticity with second sound on the semi-axis,, \emph{J. Part. Diff. Eq.}, 25 (2012), 37.
|
[8] |
Y. Hu and R. Racke, Formation of singularities in one-dimensional thermoelasticity with second sound,, \emph{Quart. Appl. Math.}, 72 (2014), 311.
doi: 10.1090/S0033-569X-2014-01336-2. |
[9] |
T. J. R. Hughes, T. Kato and J. E. Marsden, Well-posed quasi-linear second-order hyperbolic systems with applications to nonlinear elastodynamics and general relaticity,, \emph{Arch. Rational Mech. Anal.}, 63 (1977), 273.
|
[10] |
W. J. Hrusa and S. A. Messaoudi, On formation of singularities in one-dimensional nonlinear thermoelasticity,, \emph{Arch. Ration. Mech. Anal.}, 111 (1990), 135.
doi: 10.1007/BF00375405. |
[11] |
W. J. Hrusa and M. A. Tarabek, On smooth solutions of the Cauchy problem in one-dimensional nonlinear thermoelasticity,, \emph{Quart. Appl. Math.}, 47 (1989), 631.
|
[12] |
S. Jiang, Global existence and asymptotic behavior of smooth solutions in one-dimensional nonlinear thermoelasticity,, \emph{Proc. Roy. Soc. Edinburgh}, 115A (1990), 257.
doi: 10.1017/S0308210500020631. |
[13] |
S. Jiang, Global solutions of the Dirichlet problem in one-dimensional nonlinear thermoelasticity,, \emph{SFB, 138 (1990). Google Scholar |
[14] |
S. Jiang, On global smooth solutions to the one-dimensional equations of nonlnear inhomogeneous thermoelasticity,, \emph{Nonlinear Anal., 20 (1993), 1245.
doi: 10.1016/0362-546X(93)90154-K. |
[15] |
S. Jiang and R. Racke, Evolution Equations in Thermoelasticity,, Chapman and Hall/CRC Monographs and Surveys in Pure and Appl. Math. Vol. 112, (2000).
|
[16] |
A. Kasimov, R. Racke and B. Said-Houari, Global existence and decay properties for solutions of the Cauchy problem in one-dimensional thermoelasticity with second sound,, \emph{Applicable Analysis}, 93 (2014), 911.
doi: 10.1080/00036811.2013.801457. |
[17] |
T.-T, Li, Global Classical Solutions for Quasilinear Hyperbolic Systems,, Masson, (1994).
|
[18] |
S. A. Messaoudi and B. Said-Houari, Exponetial stability in one-dimensional non-linear thermoelasticity with second sound,, \emph{Math. Methods Appl. Sci.}, 28 (2005), 205.
doi: 10.1002/mma.556. |
[19] |
R. Racke and Y. Shibata, Global smooth solutions and asymptotic stability in one-dimensional nonlinear thermoelasticity,, \emph{Arch. Rational Mech. Anal.}, 116 (1991), 1.
doi: 10.1007/BF00375601. |
[20] |
R. Racke and Y. Shibada, Global solvability and exponential stability in one-dimensional nonlinear thermoelasticity,, \emph{Quart. Appl. Math.}, 51 (1993), 751.
|
[21] |
R. Racke, Thermoelasticity with second sound--Exponential stability in linear and non-linear 1-d,, \emph{Math. Meth. Appl. Sci.}, 25 (2002), 409.
doi: 10.1002/mma.298. |
[22] |
R. Racke, Thermoelasticity, Handbook of Differential Equations,, Chapter 4, (2009), 315.
doi: 10.1016/S1874-5717(08)00211-9. |
[23] |
R. Racke and Y. G. Wang, Nonlinear well-posedness and rates of decay in thermoelasticity with second sound,, \emph{J. Hyperbolic Differential Equations}, 5 (2008), 25.
doi: 10.1142/S021989160800143X. |
[24] |
J. E. M. Rivera, Energy decay rates in linear thermoelasticity,, \emph{Funkcial. Ekvac.}, 35 (1992), 19.
|
[25] |
Y. Shizuta and S. Kawashima, Systems of equations of hyperbolic-parabolic type with applications to the discrete Boltzmann equation,, \emph{Hokkaido Math. J.}, 14 (1995), 249.
doi: 10.14492/hokmj/1381757663. |
[26] |
M. A. Tarabek, On the existence of smooth solutions in one-dimensional nonlinear thermoelasticity with second sound,, \emph{Quart. Appl. Math.}, 50 (1992), 727.
|
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