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Stability analysis for linear heat conduction with memory kernels described by Gamma functions
1. | Dipartimento di Matematica “G. Castelnuovo”, Università di Roma “La Sapienza”, Piazzale A. Moro, 2, I–00185 Roma |
References:
[1] |
C. Cattaneo, Sulla conduzione del calore, Atti Semin. Mat. Fis. Univ. Modena, 3 (1949), 83-101. |
[2] |
V. V. Chepyzhov, E. Mainini and V. Pata, Stability of abstract linear semigroups arising from heat conduction with memory, Asymptot. Anal., 50 (2006), 269-291. |
[3] |
M. Conti, E. M. Marchini and V. Pata, Exponential stability for a class of linear hyperbolic equations with hereditary memory, Discrete Contin. Dyn. Syst. Ser. B, 18 (2013), 1555-1565.
doi: 10.3934/dcdsb.2013.18.1555. |
[4] |
A. Chowdury and C. I. Christov, Memory effects for the heat conductivity of random suspensions of spheres, Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., 466 (2010), 3253-3273.
doi: 10.1098/rspa.2010.0133. |
[5] |
B. R. Duffy, P. Freitas and M. Grinfeld, Memory driven instability in a diffusion process, SIAM J. Math. Anal., 33 (2002), 1090-1106 (electronic).
doi: 10.1137/S0036141001388592. |
[6] |
G. Fichera, Avere una memoria tenace crea gravi problemi, (Italian) Arch. Rational Mech. Anal., 70 (1979), 101-112.
doi: 10.1007/BF00250347. |
[7] |
C. Giorgi, M. G. Naso and V. Pata, Exponential stability in linear heat conduction with memory: A semigroup approach, Commun. Appl. Anal., 5 (2001), 121-133. |
[8] |
M. E. Gurtin and A. C. Pipkin, A general theory of heat conduction with finite wave speeds, Arch. Rational Mech. Anal., 31 (1968), 113-126.
doi: 10.1007/BF00281373. |
[9] |
D. D. Joseph and L. Preziosi, Heat waves, Rev. Modern Phys., 61 (1989), 41-73.
doi: 10.1103/RevModPhys.61.41. |
[10] |
W. E. Olmstead, S. H. Davis, S. Rosenblat and W. L. Kath, Bifurcation with memory, SIAM J. Appl. Math., 46 (1986), 171-188.
doi: 10.1137/0146013. |
[11] |
Y. Shizuta and S. Kawashima, Systems of equations of hyperbolic-parabolic type with applications to the discrete Boltzmann equation, Hokkaido Math. J., 14 (1985), 249-275.
doi: 10.14492/hokmj/1381757663. |
[12] |
H. Smith, An Introduction to Delay Differential Equations with Applications to the Life Sciences, Texts in Applied Mathematics, 57. Springer, New York, 2011.
doi: 10.1007/978-1-4419-7646-8. |
show all references
References:
[1] |
C. Cattaneo, Sulla conduzione del calore, Atti Semin. Mat. Fis. Univ. Modena, 3 (1949), 83-101. |
[2] |
V. V. Chepyzhov, E. Mainini and V. Pata, Stability of abstract linear semigroups arising from heat conduction with memory, Asymptot. Anal., 50 (2006), 269-291. |
[3] |
M. Conti, E. M. Marchini and V. Pata, Exponential stability for a class of linear hyperbolic equations with hereditary memory, Discrete Contin. Dyn. Syst. Ser. B, 18 (2013), 1555-1565.
doi: 10.3934/dcdsb.2013.18.1555. |
[4] |
A. Chowdury and C. I. Christov, Memory effects for the heat conductivity of random suspensions of spheres, Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., 466 (2010), 3253-3273.
doi: 10.1098/rspa.2010.0133. |
[5] |
B. R. Duffy, P. Freitas and M. Grinfeld, Memory driven instability in a diffusion process, SIAM J. Math. Anal., 33 (2002), 1090-1106 (electronic).
doi: 10.1137/S0036141001388592. |
[6] |
G. Fichera, Avere una memoria tenace crea gravi problemi, (Italian) Arch. Rational Mech. Anal., 70 (1979), 101-112.
doi: 10.1007/BF00250347. |
[7] |
C. Giorgi, M. G. Naso and V. Pata, Exponential stability in linear heat conduction with memory: A semigroup approach, Commun. Appl. Anal., 5 (2001), 121-133. |
[8] |
M. E. Gurtin and A. C. Pipkin, A general theory of heat conduction with finite wave speeds, Arch. Rational Mech. Anal., 31 (1968), 113-126.
doi: 10.1007/BF00281373. |
[9] |
D. D. Joseph and L. Preziosi, Heat waves, Rev. Modern Phys., 61 (1989), 41-73.
doi: 10.1103/RevModPhys.61.41. |
[10] |
W. E. Olmstead, S. H. Davis, S. Rosenblat and W. L. Kath, Bifurcation with memory, SIAM J. Appl. Math., 46 (1986), 171-188.
doi: 10.1137/0146013. |
[11] |
Y. Shizuta and S. Kawashima, Systems of equations of hyperbolic-parabolic type with applications to the discrete Boltzmann equation, Hokkaido Math. J., 14 (1985), 249-275.
doi: 10.14492/hokmj/1381757663. |
[12] |
H. Smith, An Introduction to Delay Differential Equations with Applications to the Life Sciences, Texts in Applied Mathematics, 57. Springer, New York, 2011.
doi: 10.1007/978-1-4419-7646-8. |
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