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Volumn 342, Issue 2, 2008, Pages 1052-1067

Well-posedness for the drift-diffusion system in Lp arising from the semiconductor device simulation

Author keywords

A unique time local solution; Drift diffusion model; Elliptic parabolic equations; Global solution; Hardy Littlewood Sobolev inequality; Lp spaces; Local well posedness; Positive solution; Semiconductor device; The initial boundary value problem

Indexed keywords


EID: 40649083772     PISSN: 0022247X     EISSN: 10960813     Source Type: Journal    
DOI: 10.1016/j.jmaa.2007.11.017     Document Type: Article
Times cited : (72)

References (26)
  • 1
    • 0000657461 scopus 로고    scopus 로고
    • Local and global solvability of some parabolic systems modeling chemotaxis
    • Biler P. Local and global solvability of some parabolic systems modeling chemotaxis. Adv. Math. Sci. Appl. 8 (1998) 715-743
    • (1998) Adv. Math. Sci. Appl. , vol.8 , pp. 715-743
    • Biler, P.1
  • 2
    • 0034370899 scopus 로고    scopus 로고
    • Long time behavior of solutions to Nernst-Planck and Debye-Hünkel drift-diffusion systems
    • Biler P., and Dolbeault J. Long time behavior of solutions to Nernst-Planck and Debye-Hünkel drift-diffusion systems. Ann. Henri Poincaré 1 (2000) 461-472
    • (2000) Ann. Henri Poincaré , vol.1 , pp. 461-472
    • Biler, P.1    Dolbeault, J.2
  • 3
    • 0000219814 scopus 로고
    • The Debye system: Existence and large time behavior of solutions
    • Biler P., Hebisch W., and Nadzieja T. The Debye system: Existence and large time behavior of solutions. Nonlinear Anal. 23 (1994) 1189-1209
    • (1994) Nonlinear Anal. , vol.23 , pp. 1189-1209
    • Biler, P.1    Hebisch, W.2    Nadzieja, T.3
  • 4
    • 0002854786 scopus 로고
    • Global solutions of the time-dependent drift-diffusion semiconductor equations
    • Fang W., and Ito K. Global solutions of the time-dependent drift-diffusion semiconductor equations. J. Differential Equations 123 (1995) 523-566
    • (1995) J. Differential Equations , vol.123 , pp. 523-566
    • Fang, W.1    Ito, K.2
  • 5
    • 0002756571 scopus 로고    scopus 로고
    • Solutions to a nonlinear drift-diffusion model for semiconductors
    • 38 pp. (electronic)
    • Fang W., and Ito K. Solutions to a nonlinear drift-diffusion model for semiconductors. Electron. J. Differential Equations 15 (1999) 38 pp. (electronic)
    • (1999) Electron. J. Differential Equations , vol.15
    • Fang, W.1    Ito, K.2
  • 6
    • 34250947482 scopus 로고
    • On Navier-Stokes initial value problem 1
    • Fujita H., and Kato T. On Navier-Stokes initial value problem 1. Arch. Ration. Mech. Anal. 46 (1964) 269-315
    • (1964) Arch. Ration. Mech. Anal. , vol.46 , pp. 269-315
    • Fujita, H.1    Kato, T.2
  • 7
    • 0037509741 scopus 로고
    • On the uniqueness of solutions to the drift-diffusion model of semiconductor devices
    • Gajewski H. On the uniqueness of solutions to the drift-diffusion model of semiconductor devices. Math. Models Methods Appl. Sci. 4 (1994) 121-133
    • (1994) Math. Models Methods Appl. Sci. , vol.4 , pp. 121-133
    • Gajewski, H.1
  • 8
    • 0022499052 scopus 로고
    • On the basic equations for carrier transport in semiconductors
    • Gajewski H., and Gröger K. On the basic equations for carrier transport in semiconductors. J. Math. Anal. Appl. 113 (1986) 12-35
    • (1986) J. Math. Anal. Appl. , vol.113 , pp. 12-35
    • Gajewski, H.1    Gröger, K.2
  • 9
    • 46149140458 scopus 로고
    • p and regularity of weak solutions of the Navier-Stokes system
    • p and regularity of weak solutions of the Navier-Stokes system. J. Differential Equations 61 (1986) 186-212
    • (1986) J. Differential Equations , vol.61 , pp. 186-212
    • Giga, Y.1
  • 10
    • 0001300372 scopus 로고
    • Two-dimensional Navier-Stokes flow with measure as initial vorticity
    • Giga Y., Miyakawa T., and Osada H. Two-dimensional Navier-Stokes flow with measure as initial vorticity. Arch. Ration. Mech. Anal. 104 (1988) 223-250
    • (1988) Arch. Ration. Mech. Anal. , vol.104 , pp. 223-250
    • Giga, Y.1    Miyakawa, T.2    Osada, H.3
  • 11
    • 33646866104 scopus 로고
    • Solvability and smoothing effect for semilinear parabolic equations
    • Hoshino H., and Yamada Y. Solvability and smoothing effect for semilinear parabolic equations. Funkcial. Ekvac. 34 3 (1991) 475-494
    • (1991) Funkcial. Ekvac. , vol.34 , Issue.3 , pp. 475-494
    • Hoshino, H.1    Yamada, Y.2
  • 12
    • 0000637740 scopus 로고
    • Qualitative behavior of solutions of a degenerate nonlinear drift-diffusion model for semiconductors
    • Jüngel A. Qualitative behavior of solutions of a degenerate nonlinear drift-diffusion model for semiconductors. Math. Models Methods Appl. Sci. 5 (1995) 497-518
    • (1995) Math. Models Methods Appl. Sci. , vol.5 , pp. 497-518
    • Jüngel, A.1
  • 13
    • 0000911759 scopus 로고
    • m with applications to weak solutions
    • m with applications to weak solutions. Math. Z. 187 (1984) 471-480
    • (1984) Math. Z. , vol.187 , pp. 471-480
    • Kato, T.1
  • 14
    • 0014748565 scopus 로고
    • Initiation of slime mold aggregation viewed as an instability
    • Keller E.F., and Segel L.A. Initiation of slime mold aggregation viewed as an instability. J. Theoret. Biol. 26 (1970) 399-415
    • (1970) J. Theoret. Biol. , vol.26 , pp. 399-415
    • Keller, E.F.1    Segel, L.A.2
  • 15
    • 33645699361 scopus 로고    scopus 로고
    • The uniform boundedness and threshold for the global existence of the radial solution to a drift-diffusion system
    • Kurokiba M., Nagai T., and Ogawa T. The uniform boundedness and threshold for the global existence of the radial solution to a drift-diffusion system. Comm. Pure Appl. Anal. 5 1 (2006) 97-106
    • (2006) Comm. Pure Appl. Anal. , vol.5 , Issue.1 , pp. 97-106
    • Kurokiba, M.1    Nagai, T.2    Ogawa, T.3
  • 16
    • 25844459072 scopus 로고    scopus 로고
    • Finite time blow-up of the solution for a nonlinear parabolic equation of drift-diffusion type
    • Kurokiba M., and Ogawa T. Finite time blow-up of the solution for a nonlinear parabolic equation of drift-diffusion type. Differential Integral Equations 16 4 (2003) 427-452
    • (2003) Differential Integral Equations , vol.16 , Issue.4 , pp. 427-452
    • Kurokiba, M.1    Ogawa, T.2
  • 17
    • 0000668443 scopus 로고
    • An initial value problem from semiconductor device theory
    • Mock M.S. An initial value problem from semiconductor device theory. SIAM J. Math. 5 4 (1974) 597-612
    • (1974) SIAM J. Math. , vol.5 , Issue.4 , pp. 597-612
    • Mock, M.S.1
  • 18
    • 0042727055 scopus 로고    scopus 로고
    • Global existence of solutions to a parabolic system for chemotaxis in two space dimensions
    • Nagai T. Global existence of solutions to a parabolic system for chemotaxis in two space dimensions. Nonlinear Anal. 30 (1997) 5381-5388
    • (1997) Nonlinear Anal. , vol.30 , pp. 5381-5388
    • Nagai, T.1
  • 19
    • 0035425984 scopus 로고    scopus 로고
    • Global existence and blowup of solutions to a chemotaxis system
    • Nagai T. Global existence and blowup of solutions to a chemotaxis system. Nonlinear Anal. 47 2 (2001) 777-787
    • (2001) Nonlinear Anal. , vol.47 , Issue.2 , pp. 777-787
    • Nagai, T.1
  • 20
    • 0001205112 scopus 로고    scopus 로고
    • Application of the Trudinger-Moser inequality to a parabolic system of chemotaxis
    • Nagai T., Senba T., and Yoshida K. Application of the Trudinger-Moser inequality to a parabolic system of chemotaxis. Funkcial. Ekvac. 40 3 (1997) 411-433
    • (1997) Funkcial. Ekvac. , vol.40 , Issue.3 , pp. 411-433
    • Nagai, T.1    Senba, T.2    Yoshida, K.3
  • 21
    • 40649126474 scopus 로고    scopus 로고
    • S. Odanaka, Mathematical modeling of theory of semiconductor devices, Lecture Note at Osaka University (in Japanese)
    • S. Odanaka, Mathematical modeling of theory of semiconductor devices, Lecture Note at Osaka University (in Japanese)
  • 24
    • 51249183619 scopus 로고
    • Existence and non-existence of global solutions for a semilinear heat equation
    • Weissler F. Existence and non-existence of global solutions for a semilinear heat equation. Israel J. Math. 38 (1981) 29-40
    • (1981) Israel J. Math. , vol.38 , pp. 29-40
    • Weissler, F.1
  • 25
    • 0001488448 scopus 로고    scopus 로고
    • Norm behavior of solutions to a parabolic system of chemotaxis
    • Yagi A. Norm behavior of solutions to a parabolic system of chemotaxis. Math. Jpn. 45 (1997) 241-265
    • (1997) Math. Jpn. , vol.45 , pp. 241-265
    • Yagi, A.1
  • 26
    • 0003320023 scopus 로고
    • Weakly Differentiable Functions
    • Springer-Verlag
    • Ziemer W.P. Weakly Differentiable Functions. Grad. Texts in Math. vol. 120 (1989), Springer-Verlag
    • (1989) Grad. Texts in Math. , vol.120
    • Ziemer, W.P.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.