Global well posedness for a 2D drift–diffusion–Maxwell system

References

• Delcroix JL , Bers A . Physique des plasmas. Paris: CNRS éditions; 1994.
   Google Scholar
• Markowich P . The stationary semiconductor device equations. Springer, Vienna. 1986;113.
   Google Scholar
• Selberherr S . Analysis and simulation of semiconductor devices. Wien: Springer; 1984.
   Google Scholar
• van Roosbroeck W . Theory of flow of electron and holes in germanium and other semiconductors. Bell Syst Tech J. 1950;29:560–607.
   Google Scholar
• Mock M . On equations describing steady-state carrier distributions in a semiconductor device. Commun Pure Appl Math. 1972;25(1):781–792.
   Google Scholar
• Mock M . An initial value problem from semiconductor device theory. SIAM J Math Anal. 1974;5(1):597–612.
   Google Scholar
• Fang W , Ito K . Global solutions of the time-dependent drift-diffusion semiconductor equations. J Differ Equ. 1995;123(2):523–566.
   Web of Science ®Google Scholar
• Gajewski H , Gröger K . On the basic equations for carrier transport in semiconductors. J Math Anal Appl. 1986;113(1):12–35.
   Web of Science ®Google Scholar
• Jüngel A . Qualitative behavior of solutions of a degenerate nonlinear drift-diffusion model for semiconductors. Math Models Methods Appl Sci. 1995;5(4):497–518.
   Web of Science ®Google Scholar
• Biler P , Dolbeault J . Long time behavior of solutions to Nernst-Planck and Debye-Hückel drift-diffusion systems Ann Henri Poincaré. 2000;1:461–472. Springer.
   Google Scholar
• Kurokiba M , Ogawa T . Well-posedness for the drift-diffusion system in Lp arising from the semiconductor device simulation. J Math Anal Appl. 2008;342(2):1052–1067.
   Web of Science ®Google Scholar
• Gajewski H , Gröger K . Semiconductor equations for variable mobilities based on Boltzmann statistics or Fermi-Dirac statistics. Math Nachr. 1989;140(1):7–36.
   Google Scholar
• Gröger K , Rehberg J . Uniqueness for the two-dimensional semiconductor equations in case of high carrier densities. Math Z. 1993;213(1):523–530.
   Google Scholar
• Gajewski H . On uniqueness of solutions of the drift-diffusion-model of semiconductors devices. Math Models Methods Appl Sci. 1994;4:121–139.
   Web of Science ®Google Scholar
• Jerome J . Analysis of charge transport. A mathematical study of semiconductor devices, Berlin: Springer; 1996.
   Google Scholar
• Kang E , Lee J . Notes on the global well-posedness for the Maxwell-Navier-Stokes system. Abstr Appl Anal. 2013. Article ID. 402793 (1--6).
   Google Scholar
• Masmoudi N . Global well posedness for the Maxwell-Navier-Stokes system in 2D. J Math Pures Appl. 2010;9:559–571.
   Google Scholar
• Brezzi F , Marini L , Markowich P , et al . On some numerical problems in semiconductor device simulation. Mathematical aspects of fluid and plasma dynamics (Salice Terme, 1988). Vol. 1460., Lecture notes in mathematics, Berlin: Springer; 1991. p. 31–42.
   Google Scholar
• Brezzi F , Marini L , Micheletti S , et al . Discretization of semiconductor device problem I. Vol. XIII, Handbook of numerical analysis. Amsterdam: North-Holland; 2005. p. 317–441.
   Google Scholar
• Hänsch W . The drift-diffusion equation and its applications in MOSFET modeling. Vienna: Springer; 1991.
   Google Scholar
• Jerome J . The approximation problem for drift-diffusion systems SIAM Rev. 1995;37:552–572.
   Google Scholar
• Poupaud F . Diffusion approximation of the linear semiconductor Boltzmann equation: analysis of boundary layers. Asympt Anal. 1991;4:293–317.
   Google Scholar
• Ben Abdallah N , Tayeb ML . Diffusion limit for the one dimensional Boltzmann-Poisson system. Discete Contin Dyn Syst Ser B. 2004;1129–1142.
   Web of Science ®Google Scholar
• Masmoudi N , Tayeb ML . Diffusion limit of a semiconductor Boltzmann-Poisson system. SIAM J Math Anal. 2007;36(6):1788–1807.
   Google Scholar
• Degond P , Mas-Gallic S . Existence of solutions and diffusion approximation for a model Fokker-Planck equation. Transport Theory Stat Phys. 1987;16:589–636.
   Google Scholar
• Poupaud F , Soler J . Parabolic limit and stability of the Vlasov-Fokker-Planck system. Math Models Methods Appl Sci. 2000;10(7):1027–1045.
   Web of Science ®Google Scholar
• Goudon T . Hydrodynamic limit for the Vlasov-Poisson-Fokker-Planck system: analysis of the two-dimentional case. Math Models Methods Appl Sci. 2005;15:737–752.
   Web of Science ®Google Scholar
• El Ghani N , Masmoudi N . Diffusion limit for the Vlasov-Poisson-Fokker-Planck system. Commun Math Sci. 2010;8(2):463–479.
   Web of Science ®Google Scholar
• Bostan M , Goudon T . Low field regime for the relativistic Vlasov-Maxwell-Fokker-Planck system; the one and one half dimensional case. Kinetic Related Models. 2008;1(1):139–196.
   Web of Science ®Google Scholar
• El Ghani N . Diffusion limit for the Vlasov-Maxwell-Fokker-Planck system. IAENG Int J Appl Math. 2010;40(3):159–166.
   Google Scholar
• Jochmann F . Existence of weak solutions of the drift diffusion model coupled with Maxwell’s Equations. J Math Anal Appl. 1996;204(3):655–676.
   Web of Science ®Google Scholar
• Jochmann F . Uniqueness and regularity for the two-dimensional drift-diffusion model for semiconductors coupled with Maxwell’s equations. J Differ Equ. 1998;147(2):242–270.
   Web of Science ®Google Scholar