Asymptotic behavior of solutions for the one-dimensional drift-diffusion model in the quarter plane

EDP Sciences - Tập 19 Số 2 - Trang 144-148 - 2014
Zhou, Fang1
1Department of Mathematics, Hubei University of Science and Technology, Xianning, Hubei, China

Tóm tắt

In this paper, we study the classical drift-diffusion model arising from the semiconductor device simulation, which is the simplest macroscopic model describing the dynamics of the electron and the hole. We prove the global existence of strong solutions for the initial boundary value problem in the quarter plane. In particular, we show that in large time, these solutions tend to the nonlinear diffusion wave which is different from the steady state, at an algebraic time-decay rate. As far as we know, this is the first result about the nonlinear diffusion wave phenomena of the solutions for the one-dimensional drift-diffusion model in the quarter plane.

Tài liệu tham khảo

citation_title= [M]; citation_publication_date=2001; citation_id=CR1; citation_author=A Jüngel; citation_publisher=Birkhuser citation_title= [M]; citation_publication_date=1996; citation_id=CR2; citation_author=J Jerome; citation_publisher=Springer-Verlag citation_title= [M]; citation_publication_date=1990; citation_id=CR3; citation_author=P A Markowich; citation_author=C A Ringhofev; citation_author=C Schmeiser; citation_publisher=Springer-Verlag citation_journal_title=Math Methods Appl Sci; citation_title=Stationary solutions to the drift-diffusion model in the whole spaces [J]; citation_author=R Kobayashi, M Kurokiba, S Kawashima; citation_volume=32; citation_publication_date=2009; citation_pages=640-652; citation_doi=10.1002/mma.1058; citation_id=CR4 citation_journal_title=SIAM J Math Anal; citation_title=An initial value problem from semiconductor device theory [J]; citation_author=M S Mock; citation_volume=5; citation_publication_date=1974; citation_pages=597-612; citation_doi=10.1137/0505061; citation_id=CR5 citation_journal_title=J Math Anal Appl; citation_title=Asymptotic behavior of solutions of transport equations for semiconductor devices simulation[J]; citation_author=M S Mock; citation_volume=49; citation_publication_date=1975; citation_pages=215-225; citation_doi=10.1016/0022-247X(75)90172-9; citation_id=CR6 citation_journal_title=Electron J Differential Equations; citation_title=Solutions to a nonlinear drift-diffusion model for semiconductors [J]; citation_author=W Fang, K Ito; citation_volume=15; citation_publication_date=1999; citation_pages=38; citation_id=CR7 citation_journal_title=J Differential Equations; citation_title=Global solutions of the time-dependent drift-diffusion model semiconductor equations [J]; citation_author=W Fang, K Ito; citation_volume=123; citation_publication_date=1995; citation_pages=523-566; citation_doi=10.1006/jdeq.1995.1172; citation_id=CR8 citation_journal_title=J Differential Equations; citation_title=Asymptotic behavior of the drift-diffusion semiconductor equations [J]; citation_author=W Fang, K Ito; citation_volume=123; citation_publication_date=1995; citation_pages=567-587; citation_doi=10.1006/jdeq.1995.1173; citation_id=CR9 citation_journal_title=Math Models Methods Appl Sci; citation_title=On the uniqueness of solutions to the drift-diffusion model of semiconductor devices [J]; citation_author=H Gajewski; citation_volume=4; citation_publication_date=1994; citation_pages=121-133; citation_doi=10.1142/S021820259400008X; citation_id=CR10 citation_journal_title=J Math Anal Appl; citation_title=On the basic equations for carrier transport in semiconductors [J]; citation_author=H Gajewski, K Groger; citation_volume=113; citation_publication_date=1986; citation_pages=12-35; citation_doi=10.1016/0022-247X(86)90330-6; citation_id=CR11 citation_journal_title=Math Models Methods Appl Sci; citation_title=On the existence and uniqueness of transient solutions of a degenerate nonlinear drift-diffusion model for semiconductors [J]; citation_author=A Jüngel; citation_volume=4; citation_publication_date=1994; citation_pages=677-703; citation_doi=10.1142/S0218202594000388; citation_id=CR12 citation_journal_title=J Math Anal Appl; citation_title=Well-posedness for the drift-diffusion system in Lp arising from the semiconductor device simulation [J]; citation_author=M Kurokiba, T Ogawa; citation_volume=342; citation_publication_date=2008; citation_pages=1052-1067; citation_doi=10.1016/j.jmaa.2007.11.017; citation_id=CR13 citation_journal_title=Z Angew Math Phys; citation_title=Zero-relaxation-time limits in hydrodynamic models for plasmas revisted [J]; citation_author=A Jüngel, Y J Peng; citation_volume=51; citation_publication_date=2000; citation_pages=385-396; citation_doi=10.1007/s000330050004; citation_id=CR14 citation_journal_title=J Math Anal Appl; citation_title=The bipolar hydrodynamic model for semiconductors and the drift-diffusion equation [J]; citation_author=R Natalini; citation_volume=198; citation_publication_date=1996; citation_pages=262-281; citation_doi=10.1006/jmaa.1996.0081; citation_id=CR15 citation_journal_title=Math Models Methods Appl Sci; citation_title=The global weak solution and relaxation limits of the initial boundary value problem to the bipolar hydrodynamic model for semiconductors [J]; citation_author=L Hsiao, K J Zhang; citation_volume=10; citation_publication_date=2000; citation_pages=1333-1361; citation_doi=10.1142/S0218202500000653; citation_id=CR16 citation_journal_title=J Differential Equations; citation_title=Large time behavior of solutions of the bipolar hydrodynamical model for semiconductors [J]; citation_author=I Gasser, L Hsiao, H L Li; citation_volume=192; citation_publication_date=2003; citation_pages=326-359; citation_doi=10.1016/S0022-0396(03)00122-0; citation_id=CR17 citation_journal_title=Dis Cont Dyn Sys; citation_title=Large time behavior and quasineutral limit of solutions to a bipolar hydrodynamic model with large data and vacuum [J]; citation_author=F M Huang, Y P Li; citation_volume=A24; citation_publication_date=2009; citation_pages=455-470; citation_id=CR18 citation_journal_title=J Math Phys; citation_title=Long-time self-similar asymptotic of the macroscopic quantum models [J]; citation_author=H L Li, G J Zhang, M Zhang; citation_volume=49; citation_publication_date=2008; citation_pages=073503; citation_doi=10.1063/1.2949082; citation_id=CR19 citation_journal_title=J Math Fluid Mech; citation_title=Optimal convergence rates to diffusion waves for solutions of the hyperbolic conservation laws with damping [J]; citation_author=P Marcati, M Mei, B Rubino; citation_volume=7; citation_publication_date=2005; citation_pages=S224-S240; citation_doi=10.1007/s00021-005-0155-9; citation_id=CR20 citation_journal_title=J Differential Equations; citation_title=Convergence rates to nonlinear diffusion waves for solutions of system of hyperbolic conservation laws with damping [J]; citation_author=K Nishihara; citation_volume=131; citation_publication_date=1996; citation_pages=171-188; citation_doi=10.1006/jdeq.1996.0159; citation_id=CR21