Citation: |
[1] |
N. Ben Abdallah, Weak solutions of the initial-boundary value problem for the Vlasov-Poisson system, Math. Meth. in the Appl. Sci., 17 (1994), 451-476.doi: 10.1002/mma.1670170604. |
[2] |
N. Ben Abdallah and P. Degond, On a hierarchy of macroscopic models for semiconductors, J. Math. Phys., 37 (1996), 3306-3333.doi: 10.1063/1.531567. |
[3] |
N. Ben Abdallah and J. Dolbeault, Relative entropies for the Vlasov-Poisson system in bounded domains, C. R. Acad. Sci. Paris Ser. I Math., 330 (2000), 867-872.doi: 10.1016/S0764-4442(00)00268-8. |
[4] |
N. Ben Abdallah, P. Degond, P. Markowich and C. Schmeiser, High field approximations of the spherical harmonics expansion model for semiconductors, ZAMP, 52 (2001), 201-230.doi: 10.1007/PL00001544. |
[5] |
N. Ben Abdallah and M. L. Tayeb, Diffusion approximation for the one dimensional Boltzmann-Poisson system, DCDS-B, 4 (2004), 1129-1142.doi: 10.3934/dcdsb.2004.4.1129. |
[6] |
H. Brezis, "Analyse Fonctionnelle, Théorie et Applications,'' Collection Mathématiques Appliquées pour la Maîtrise, Masson, Paris, 1983. |
[7] |
D. Chen, E. C. Kan, U. Ravaioli, C. Shu and R. W. Dutton, An improved energy transport model including non-parabolicity and non-Maxwellian distribution effects, IEEE Electron Dev. Lett., 13 (1992), 235-239. |
[8] |
C. Cercignani, R. Illner, M. Pulvirenti, "The Mathematical Theory of Dilute Gases,'' Applied Mathematical Sciences, 106, Springer-Verlag, New York, 1994. |
[9] |
P. Degond and S. Schmeiser, Macroscopic models for semiconductor heterostructures, J. Math. Phys., 39 (1998), 4634-4663.doi: 10.1063/1.532528. |
[10] |
L. C. Evans, "Partial Differential Equations,'' Graduate Studies in Mathematics, 19, American Mathematical Society, Providence, Rhode Island, 1998. |
[11] |
H. Grad, Asymptotic theory of the Boltzmann equation, Phys. Fluids, 6 (1963), 147-181.doi: 10.1063/1.1706716. |
[12] |
H. Grad, Principles of the kinetic theory of gases, in "Handbuch der Physik" (herausgegeben von S. Flügge), Bd. 12, Thermodynamik der Gase, Springer-Verlag, Berlin-Göttingen-Heidelberg, (1958), 205-294. |
[13] |
E. Lyumkis, B. Polsky, A. Shur and P. Visocky, Transient semiconductor device simulation including energy balance equation, COMPEL, 11 (1992), 311-325. |
[14] |
P. A. Markowich, F. Popaud and C. Schmeiser, Diffusion approximation of nonlinear electron phonon collision mechanisms, RAIRO Modél. Math. Anal. Num., 29 (1995), 857-869. |
[15] |
P. A. Markowich, C. Ringhofer and C. Schmeiser, "Semiconductor Equations,'' Springer-Verlag, Vienna, 1990.doi: 10.1007/978-3-7091-6961-2. |
[16] |
N. Masmoudi and M. L. Tayeb, Diffusion limit of a semiconductor Boltzmann-Poisson system, SIAM J. Math. Anal., 38 (2007), 1788-1807.doi: 10.1137/050630763. |
[17] |
M. L. Tayeb, From Boltzmann equation to spherical harmonics expansion model: Diffusion limit and Poisson coupling, Comm. Math. Sci., 9 (2011), 255-275. |