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Optimality of piecewise thermal conductivity in a snow-ice thermodynamic system
1. | Department of Mathematics, Shanghai University, Shanghai 200444, China, China |
References:
[1] |
N. Calonne, F. Flin, S. Morin, B. Lesaffre, S. du Roscoat, C. Geindreau, F. St Martin dHeres, F. Grenoble and I. Grenoble, Numerical and experimental investigations of the effective thermal conductivity of snow, J. Geophys. Res., 38 (2010), L23501.
doi: 10.1029/2011GL049234. |
[2] |
C. I. Christov and T. Marinov, Identification of heat-conduction coefficient via method of variational imbedding, Math. Comput. Modell., 27 (1998), 109-116.
doi: 10.1016/S0895-7177(97)00269-0. |
[3] |
S. Dutman and J. Ha, Identifiability of piecewise constant conductivity in a heat conduction process, SIAM J.Control.Optim., 46 (2007), 694-713.
doi: 10.1137/060657364. |
[4] |
H. W. Engl and J. Zou, A new approach to convergence rate analysis of Tikhonov regularization for parameter identification in heat conduction, Inverse Probl., 16 (2000), 1907-1923.
doi: 10.1088/0266-5611/16/6/319. |
[5] |
L. C Evans, Partial differential equations, 2nd edition, Graduate studies in mathemastic 19. Province, RI: American Mathemastic Society, 2010, 350-358. |
[6] |
H. Fang, J. Wang, E. Feng and Z. Li, Parameter identification and application of a distributed parameter coupled system with a movable inner boundary, Computers and Mathematics with Applications, 62 (2011), 4015-4020.
doi: 10.1016/j.camwa.2011.09.035. |
[7] |
T. Fichefet, B. Tartinville and H. Goosse, Sensitivity of the Antarctic sea ice to the thermal conductivity of snow, Geophys. Res. Lett., 27 (2000), 401-404. |
[8] |
S. Gutman, Identification of discontinuous parameter in flow equation, SIAM J.Control Optim., 28 (1990), 1049-1060.
doi: 10.1137/0328057. |
[9] |
S. Larrsson and V. Themée, Partial differential equations with numerical methods, Springer-Verlag, New York, 1971. |
[10] |
RO. Lecomte, T. Fichefet, M. Vancoppenolle, F. Domine, F. Massonnet, P. Mathiot, S. Morin and P. Y. Barriat, On the formulation of snow thermal conductivity in large-scale sea ice models, J. Adv. Model. Earth Syst., 5 (2013).
doi: 10.1002/jame.20039. |
[11] |
R. Lei, Z. Li, B. Cheng, Z. Zhang and P. Heil, Annual cycle of landfast sea ice in Prydz Bay, east Antarctica, Geophys. Res. Lett., 115 (2010), C02006.
doi: 10.1029/2008JC005223. |
[12] |
P. Lemke, W. Owens and W. D. Hibler III, A coupled sea ice-mixed layer-pycnocline model for the Weddell Sea, J. Geophys. Res., 95 (1990), 9513-9525. |
[13] |
W. Lv, E. Feng and Z. Li, A coupled thermodynamic system of sea ice and its parameter identification, Appl. Math. Model., 32 (2008), 1198-1207.
doi: 10.1016/j.apm.2007.03.006. |
[14] |
W. Lv, E. Feng and Z. Li, Properties and optimality conditions of a three-dimension non-smooth thermodynamic system of sea ice, Appl. Math. Model., 33 (2009), 2324-2333.
doi: 10.1016/j.apm.2008.07.002. |
[15] |
G. A. Maykut and W. M. Washington, Some results from a time-dependent thermodynamic model of sea ice, J. Geophys. Res., 276 (1971), 1550-1575. |
[16] |
M. J. McGuinness, K. Collins, H. J. Trodahl and T. G. Haskell, Nonlinear thermal transport and brine convection in first year sea ice, Ann. Glaciol., 72 (1998), 471-476. |
[17] |
S. Omatu and J. H. Seinfeld, Distributed parameter system, Cla.Press, 274 (1989), Oxford. |
[18] |
C. L. Parkinson and W. M. Washington, A large-scale numerical model of sea ice, J. Geophys. Res., 84 (1979), 311-337. |
[19] |
D. J. Pringle, H. Eicken, H. J. Trodahl and L. G. E. Backstrom, Thermal conductivity of landfast Antarctic and Arctic sea ice, J. Geophys. Res., 112 (2007), C04017.
doi: 10.1029/2006JC003641. |
[20] |
M. C. Serreze, M. M. Holland and J. Stroeve, Perspectives on the Arctic's shrinking sea-ice cover, Science, 315 (2007), 1533-1536. |
[21] |
H. J. Trodahl, S. Wilkinson, M. McGuinness and T. Haskell, Thermal conductivity of sea ice: Dependence on temperature and depth, Geophys. Res. Lett., 28 (2001), 1279-1282. |
[22] |
X. Wu, I. Simmonds and W. Budd, Modeling of Antarctic sea ice in a general circulation model, J. Clim., 10 (1997), 593-609. |
[23] |
C. Y. Yang, Estimation of the temperature-dependent thermal conductivity in inverse heat condition problems, Appl. Math. Modell., 23 (1999), 469-478. |
show all references
References:
[1] |
N. Calonne, F. Flin, S. Morin, B. Lesaffre, S. du Roscoat, C. Geindreau, F. St Martin dHeres, F. Grenoble and I. Grenoble, Numerical and experimental investigations of the effective thermal conductivity of snow, J. Geophys. Res., 38 (2010), L23501.
doi: 10.1029/2011GL049234. |
[2] |
C. I. Christov and T. Marinov, Identification of heat-conduction coefficient via method of variational imbedding, Math. Comput. Modell., 27 (1998), 109-116.
doi: 10.1016/S0895-7177(97)00269-0. |
[3] |
S. Dutman and J. Ha, Identifiability of piecewise constant conductivity in a heat conduction process, SIAM J.Control.Optim., 46 (2007), 694-713.
doi: 10.1137/060657364. |
[4] |
H. W. Engl and J. Zou, A new approach to convergence rate analysis of Tikhonov regularization for parameter identification in heat conduction, Inverse Probl., 16 (2000), 1907-1923.
doi: 10.1088/0266-5611/16/6/319. |
[5] |
L. C Evans, Partial differential equations, 2nd edition, Graduate studies in mathemastic 19. Province, RI: American Mathemastic Society, 2010, 350-358. |
[6] |
H. Fang, J. Wang, E. Feng and Z. Li, Parameter identification and application of a distributed parameter coupled system with a movable inner boundary, Computers and Mathematics with Applications, 62 (2011), 4015-4020.
doi: 10.1016/j.camwa.2011.09.035. |
[7] |
T. Fichefet, B. Tartinville and H. Goosse, Sensitivity of the Antarctic sea ice to the thermal conductivity of snow, Geophys. Res. Lett., 27 (2000), 401-404. |
[8] |
S. Gutman, Identification of discontinuous parameter in flow equation, SIAM J.Control Optim., 28 (1990), 1049-1060.
doi: 10.1137/0328057. |
[9] |
S. Larrsson and V. Themée, Partial differential equations with numerical methods, Springer-Verlag, New York, 1971. |
[10] |
RO. Lecomte, T. Fichefet, M. Vancoppenolle, F. Domine, F. Massonnet, P. Mathiot, S. Morin and P. Y. Barriat, On the formulation of snow thermal conductivity in large-scale sea ice models, J. Adv. Model. Earth Syst., 5 (2013).
doi: 10.1002/jame.20039. |
[11] |
R. Lei, Z. Li, B. Cheng, Z. Zhang and P. Heil, Annual cycle of landfast sea ice in Prydz Bay, east Antarctica, Geophys. Res. Lett., 115 (2010), C02006.
doi: 10.1029/2008JC005223. |
[12] |
P. Lemke, W. Owens and W. D. Hibler III, A coupled sea ice-mixed layer-pycnocline model for the Weddell Sea, J. Geophys. Res., 95 (1990), 9513-9525. |
[13] |
W. Lv, E. Feng and Z. Li, A coupled thermodynamic system of sea ice and its parameter identification, Appl. Math. Model., 32 (2008), 1198-1207.
doi: 10.1016/j.apm.2007.03.006. |
[14] |
W. Lv, E. Feng and Z. Li, Properties and optimality conditions of a three-dimension non-smooth thermodynamic system of sea ice, Appl. Math. Model., 33 (2009), 2324-2333.
doi: 10.1016/j.apm.2008.07.002. |
[15] |
G. A. Maykut and W. M. Washington, Some results from a time-dependent thermodynamic model of sea ice, J. Geophys. Res., 276 (1971), 1550-1575. |
[16] |
M. J. McGuinness, K. Collins, H. J. Trodahl and T. G. Haskell, Nonlinear thermal transport and brine convection in first year sea ice, Ann. Glaciol., 72 (1998), 471-476. |
[17] |
S. Omatu and J. H. Seinfeld, Distributed parameter system, Cla.Press, 274 (1989), Oxford. |
[18] |
C. L. Parkinson and W. M. Washington, A large-scale numerical model of sea ice, J. Geophys. Res., 84 (1979), 311-337. |
[19] |
D. J. Pringle, H. Eicken, H. J. Trodahl and L. G. E. Backstrom, Thermal conductivity of landfast Antarctic and Arctic sea ice, J. Geophys. Res., 112 (2007), C04017.
doi: 10.1029/2006JC003641. |
[20] |
M. C. Serreze, M. M. Holland and J. Stroeve, Perspectives on the Arctic's shrinking sea-ice cover, Science, 315 (2007), 1533-1536. |
[21] |
H. J. Trodahl, S. Wilkinson, M. McGuinness and T. Haskell, Thermal conductivity of sea ice: Dependence on temperature and depth, Geophys. Res. Lett., 28 (2001), 1279-1282. |
[22] |
X. Wu, I. Simmonds and W. Budd, Modeling of Antarctic sea ice in a general circulation model, J. Clim., 10 (1997), 593-609. |
[23] |
C. Y. Yang, Estimation of the temperature-dependent thermal conductivity in inverse heat condition problems, Appl. Math. Modell., 23 (1999), 469-478. |
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