Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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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
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Abstract | References | Similar Articles | Additional Information

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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  • [1] N. Ben Abdallah and P. Degond, On a hierarchy of macroscopic models for semiconductor, J. Math. Phys., 37 (1996), 3383-3333. MR 1401227
  • [2] 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. MR 1401255
  • [3] E. Lyumkis, B. Polsky, A. Shur, and D. Visocky, Transient semiconductor device simulation including energy balance equation, Compel, 11 (1992), 311-325.
  • [4] L. Chen and L. Hsiao, Mixed Boundary Value Problem of Stationary Energy Transport Model, preprint.
  • [5] L. Chen and L. Hsiao, The Solution of Lyumkis Energy Transport Model in Semiconductor Science, preprint. MR 2009462
  • [6] 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. MR 1648515
  • [7] 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.
  • [8] 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. MR 1656815
  • [9] 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. MR 1667190
  • [10] 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. MR 1815191
  • [11] A. Jüngel, Regularity and uniqueness of solutions to a parabolic system in nonequilibrium thermodynamics, Nonlin. Anal. 41 (2000), 669-688.
  • [12] A. Jüngel, Quasi-hydrodynamic semiconductor equations, Basel; Boston; Berlin; Birkhäuser, 2001.
  • [13] A. Jüngel, Macroscopic models for semiconductor devices. A review, preprint.
  • [14] 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. MR 1308468

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DOI: https://doi.org/10.1090/qam/2054603
Article copyright: © Copyright 2004 American Mathematical Society

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