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: 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 .

**[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, 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