Skip to main content
Log in

Local existence result in time for a drift-diffusion system with Robin boundary conditions

  • Published:
Zeitschrift für angewandte Mathematik und Physik Aims and scope Submit manuscript

Abstract

This paper deals with a drift-diffusion system being subjected to Robin boundary conditions. Under appropriate hypotheses on the data, a local existence result in time is obtained by using a fixed-point argument combined with some a priori estimates.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Blanchet, A., Carrillo, J.A., Masmoudi, N.: Infinite time aggregation for the critical Patlak-Keller-Segel model in \({\mathbb{R}}^2\). Commun. Pure Appl. Math. 61(19), 1449–1481 (2008)

    Article  Google Scholar 

  2. Brezis, H.: Analyse fonctionnelle. Collection Mathématiques Appliquées pour la Maîtrise. Masson, Paris. Théorie et applications (1983)

  3. Brezzi, F., Marini, L.D., Pietra, P.: Numerical simulation of semiconductor devices. Comput. Methods Appl. Mech. Eng. 75, 493–514 (1989)

    Article  MathSciNet  Google Scholar 

  4. Ciuperca, I.S., Heibig, A., Palade, L.I.: Existence and uniqueness results for the Doi-Edwards polymer melt model: the case of the (full) nonlinear configurational probability density equation. Nonlinearity 25(4), 991–1009 (2012)

    Article  MathSciNet  Google Scholar 

  5. Chen, Z., Cockburn, B.: Analysis of a finite element method for the drift-diffusion semiconductor device equations: the multidimensional case. Numer. Math. 71, 1–28 (1995)

    Article  MathSciNet  Google Scholar 

  6. Constantin, P., Masmoudi, N.: Global well-posedness for a Smoluchowski equation coupled with Navier–Stokes equations in 2D. Commun. Math. Phys. 278(1), 179–191 (2008)

    Article  MathSciNet  Google Scholar 

  7. Constantin, P., Seregin, G.: Global regularity of solutions of coupled Navier–Stokes equations and nonlinear Fokker Planck equations. Discrete Contin. Dyn. Syst. 26(4), 1185–1196 (2010)

    Article  MathSciNet  Google Scholar 

  8. Da Veiga, H.B.: On semiconductor drift-diffusion equations. Differ. Int. Eqs. 9, 729–744 (1996)

    MathSciNet  MATH  Google Scholar 

  9. Fang, W., Ito, K.: Global solutions of the time-dependent drift-diffusion semiconductor equations. J. Differ. Equ. 123(2), 523–566 (1995)

    Article  MathSciNet  Google Scholar 

  10. Fang, W., Ito, K.: On the time-dependent drift-diffusion model for semiconductors. J. Differ. Equ. 117(2), 245–280 (1995)

    Article  MathSciNet  Google Scholar 

  11. Gajewski, H.: On existence, uniqueness and asymptotic behavior of solutions of the basic equations for carrier transport in semiconductors. Z. Angew. Math. Mech. 65(2), 101–108 (1985)

    Article  MathSciNet  Google Scholar 

  12. Gajewski, H.: On the uniqueness of solutions to the drift-diffusion model of semi-conductors devices. Math. Models Methods Appl. Sci. 4, 121–133 (1994)

    Article  MathSciNet  Google Scholar 

  13. Heibig, A.: Well-posedness of a Debye type system endowed with a full wave equation. Appl. Math. Lett. 81, 27–34 (2018)

    Article  MathSciNet  Google Scholar 

  14. Keller, E.F., Segel, L.A.: Initiation of slime mold aggregation viewed as an instability. J. Theor. Biol. 26, 399–415 (1970)

    Article  MathSciNet  Google Scholar 

  15. Marcati, P., Natalini, R.: Weak solutions to a hydrodynamic model for semiconductors and relaxation to the drift-diffusion equation. Arch. Ration. Mech. Anal. 129(2), 129–145 (1995)

    Article  MathSciNet  Google Scholar 

  16. Markowich, P.A.: The stationary semiconductor device equations, p. ix+193. Springer, Vienna (1990)

    Book  Google Scholar 

  17. Mock, M.S.: Analysis of mathematical models of semiconductor devices. In: Advances in Numerical Computation Series, vol 3, pp. viii+200. Boole Press (1983)

  18. Mizoguchi, N.: Global existence for the Cauchy problem of the parabolic–parabolic Keller–Segel system on the plane. Calc. Var. Partial Differ. Equ. 48, 491–505 (2013)

    Article  MathSciNet  Google Scholar 

  19. Scharfetter, D.L., Gummel, H.K.: Large signal analysis of a silicon read diode oscillator. IEEE Trans. Electron. Dev. 16, 64–77 (1969)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Arnaud Heibig.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Heibig, A., Petrov, A. Local existence result in time for a drift-diffusion system with Robin boundary conditions. Z. Angew. Math. Phys. 70, 162 (2019). https://doi.org/10.1007/s00033-019-1206-z

Download citation

  • Received:

  • Revised:

  • Published:

  • DOI: https://doi.org/10.1007/s00033-019-1206-z

Mathematics Subject Classification

Keywords

Navigation