TY - JOUR
T1 - Diffusion and homogenization approximation for semiconductor boltzmann-poisson system
AU - Masmoudi, Nader
AU - Tayeb, Mohamed Lazhar
N1 - Funding Information:
N. M. is partially supported by an NSF grant DMS-0703145.
PY - 2008/3
Y1 - 2008/3
N2 - In this paper, the diffusion and homogenization approximation of the Boltzmann-Poisson system in the presence of a spatially oscillating electrostatic potential is studied. By analyzing the relative entropy, the uniform energy estimate for a well-prepared boundary data is proved. An averaging lemma and two-scale convergence techniques are used to prove rigorously the convergence of the scaled Boltzmann equation (coupled to Poisson) to a homogenized drift-diffusion-Poisson system.
AB - In this paper, the diffusion and homogenization approximation of the Boltzmann-Poisson system in the presence of a spatially oscillating electrostatic potential is studied. By analyzing the relative entropy, the uniform energy estimate for a well-prepared boundary data is proved. An averaging lemma and two-scale convergence techniques are used to prove rigorously the convergence of the scaled Boltzmann equation (coupled to Poisson) to a homogenized drift-diffusion-Poisson system.
KW - Averaging lemma
KW - Boltzmann-Poisson system
KW - Diffusion approximation
KW - Drift-diffusion equation
KW - Homogenization
KW - Renormalized solution
KW - Semiconductors
KW - Two-scale convergence
UR - http://www.scopus.com/inward/record.url?scp=44049095977&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=44049095977&partnerID=8YFLogxK
U2 - 10.1142/S0219891608001374
DO - 10.1142/S0219891608001374
M3 - Article
AN - SCOPUS:44049095977
SN - 0219-8916
VL - 5
SP - 65
EP - 84
JO - Journal of Hyperbolic Differential Equations
JF - Journal of Hyperbolic Differential Equations
IS - 1
ER -