Global existence and asymptotic behavior to the solutions of 1-D Lyumkis energy transport model for semiconductors
Authors:
Li Chen, Ling Hsiao and Yong Li
Journal:
Quart. Appl. Math. 62 (2004), 337-358
MSC:
Primary 82D37; Secondary 35K55, 35K65, 76X05
DOI:
https://doi.org/10.1090/qam/2054603
MathSciNet review:
MR2054603
Full-text PDF Free Access
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Abstract: The global existence and asymptotic behavior of smooth solutions to the initial-boundary value problem for the 1-D Lyumkis energy transport model in semiconductor science is studied. When the boundary is insulated, the smooth solution of the problem converges to a stationary solution of the drift diffusion equations, exponentially fast as $t \to \infty$.
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- N. Ben Abdallah, P. Degond, and S. Genieys, An energy-transport model for semiconductors derived from the Boltzmann equation, J. Statist. Phys. 84 (1996), no. 1-2, 205–231. MR 1401255, DOI https://doi.org/10.1007/BF02179583
E. Lyumkis, B. Polsky, A. Shur, and D. Visocky, Transient semiconductor device simulation including energy balance equation, Compel, 11 (1992), 311–325.
L. Chen and L. Hsiao, Mixed Boundary Value Problem of Stationary Energy Transport Model, preprint.
- Li Chen and Ling Hsiao, The solution of Lyumkis energy transport model in semiconductor science, Math. Methods Appl. Sci. 26 (2003), no. 16, 1421–1433. MR 2009462, DOI https://doi.org/10.1002/mma.430
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P. Degond, S. Génieys, and A. Jüngel, A system of parabolic equations in nonequilibrium thermodynamics including thermal and electrical effects, J. Math. Pures Appl. 76 (1997), 991–1015.
- S. Génieys, Energy-transport model for a nondegenerate semiconductor: convergence of the Hilbert expansion in the linearized case, Asymptot. Anal. 17 (1998), no. 4, 279–308. MR 1656815
- J. A. Griepentrog, An application of the implicit function theorem to an energy model of the semiconductor theory, ZAMM Z. Angew. Math. Mech. 79 (1999), no. 1, 43–51 (English, with English and German summaries). MR 1667190, DOI https://doi.org/10.1002/%28SICI%291521-4001%28199901%2979%3A1%3C43%3A%3AAID-ZAMM43%3E3.3.CO%3B2-3
- Ling Hsiao and Tong Yang, Asymptotics of initial boundary value problems for hydrodynamic and drift diffusion models for semiconductors, J. Differential Equations 170 (2001), no. 2, 472–493. MR 1815191, DOI https://doi.org/10.1006/jdeq.2000.3825
A. Jüngel, Regularity and uniqueness of solutions to a parabolic system in nonequilibrium thermodynamics, Nonlin. Anal. 41 (2000), 669–688.
A. Jüngel, Quasi-hydrodynamic semiconductor equations, Basel; Boston; Berlin; Birkhäuser, 2001.
A. Jüngel, Macroscopic models for semiconductor devices. A review, preprint.
- Hong Xie, $L^{2,\mu }(\Omega )$ estimate to the mixed boundary value problem for second order elliptic equations and its application in the thermistor problem, Nonlinear Anal. 24 (1995), no. 1, 9–27. MR 1308468, DOI https://doi.org/10.1016/0362-546X%2894%29E0038-I
N. Ben Abdallah and P. Degond, On a hierarchy of macroscopic models for semiconductor, J. Math. Phys., 37 (1996), 3383–3333.
N. Ben Abdallah, P. Degond, and S. Génieys, An energy-transport model for semiconductors derived from the Boltzmann equation, J. Stat. Phys., 84 (1996), 205–231.
E. Lyumkis, B. Polsky, A. Shur, and D. Visocky, Transient semiconductor device simulation including energy balance equation, Compel, 11 (1992), 311–325.
L. Chen and L. Hsiao, Mixed Boundary Value Problem of Stationary Energy Transport Model, preprint.
L. Chen and L. Hsiao, The Solution of Lyumkis Energy Transport Model in Semiconductor Science, preprint.
P. Degond, S. Génieys, and A. Jüngel, A steady-state system in nonequilibrium thermodynamics including thermal and electrical effects, Math. Meth. Appl. Sci., 21 (1998) 1399–1413.
P. Degond, S. Génieys, and A. Jüngel, A system of parabolic equations in nonequilibrium thermodynamics including thermal and electrical effects, J. Math. Pures Appl. 76 (1997), 991–1015.
S. Génieys, Energy transport model for a non degenerate semiconductor. Convergence of the Hilbert expansion in the linearized case, Asympt. Anal., 17 (1998), 279–308.
J. A. Griepentrog, An application of the implicit function theorem to an energy model of the semiconductor theory, Z. Angew. Math. Mech., 79 (1999), 43–51.
L. Hsiao and T. Yang, Asymptotics of initial boundary value problems for hydrodynamic and drift diffusion models for semiconductors, J. Diff. Eqns., 170 (2001), 472–493.
A. Jüngel, Regularity and uniqueness of solutions to a parabolic system in nonequilibrium thermodynamics, Nonlin. Anal. 41 (2000), 669–688.
A. Jüngel, Quasi-hydrodynamic semiconductor equations, Basel; Boston; Berlin; Birkhäuser, 2001.
A. Jüngel, Macroscopic models for semiconductor devices. A review, preprint.
H. Xie, ${L^{2, \mu }}\left ( \Omega \right )$ estimate to the mixed boundary value problem for second order elliptic equations and its application in the thermistor problem, Nonlinear Anal. 24, (1995), 9–27.
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© Copyright 2004
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