Free Access
Issue
ESAIM: COCV
Volume 18, Number 4, October-December 2012
Page(s) 1097 - 1121
DOI https://doi.org/10.1051/cocv/2011191
Published online 16 January 2012
  1. P. Biler and J. Dolbeault, Long time behavior of solutions to Nernst-Planck and Debye-Hückel drift-diffusion system. Ann. Henri Poincaré 1 (2000) 461−472. [CrossRef] [MathSciNet]
  2. P. Biler and N. Nadzieja, Existence and nonexistence of solutions for a model of gravitational interactions of particles I. Colloq. Math. 66 (1994) 319−334. [MathSciNet]
  3. P. Biler and N. Nadzieja, A singular problem in electrolytes theory. Math. Methods Appl. Sci. 20 (1997) 767–782. [CrossRef]
  4. P. Biler, G. Karch, P. Laurençot and T. Nadzieja, The 8π-problem for radially symmetric solutions of a chemotaxis model in the plane. Math. Methods Appl. Sci. 29 (2006) 1563–1583. [CrossRef] [MathSciNet]
  5. S. Childress and J.K. Percus, Nonlinear aspects of chemotaxis, Math. Biosci. 56 (1981) 217–237. [CrossRef] [MathSciNet]
  6. R. Farwig and H. Sohr, Weighted Lq-theory for the Stokes resolvent in exterior domains. J. Math. Soc. Jpn 49 (1997) 251–288. [CrossRef]
  7. M. Escobedo and E. Zuazua, Large time behavior for convection-diffusion equations in ℝN. J. Funct. Anal. 100 (1991) 119–161. [CrossRef] [MathSciNet]
  8. S. Kawashima, S. Nishibata and M. Nishikawa, Lp energy method for multi-dimensional viscous conservation laws and application to the stability of planar waves. J. Hyperbolic Differ. Equ. 1 (2004) 581–603. [CrossRef] [MathSciNet]
  9. E.F. Keller and L.A. Segel, Initiation of slime mold aggregation viewed as an instability, J. Theor. Biol. 26 (1970) 399–415. [CrossRef] [PubMed]
  10. R. Kobayashi and S. Kawashima, Decay estimates and large time behavior of solutions to the drift-diffusion system. Funkcial. Ekvac. 51 (2008) 371–394. [CrossRef] [MathSciNet]
  11. R. Kobayashi, M. Kurokiba and S. Kawashima, Stationary solutions to the drift-diffusion model in the whole space. Math. Methods Appl. Sci. 32 (2009) 640–652. [CrossRef]
  12. M. Kurokiba and T. Ogawa, Lp wellposedness for the drift-diffusion system arising from the semiconductor device simulation. J. Math. Anal. Appl. 342 (2008) 1052–1067. [CrossRef]
  13. D.S. Kurtz and R.L. Wheeden, Results on weighted norm inequalities for multipliers, Trans. Amer. Math. Soc. 255 (1979) 343–362. [CrossRef] [MathSciNet]
  14. M.S. Mock, Asymptotic behavior of solutions of transport equations for semiconductor devices, J. Math. Anal. Appl. 49 (1975) 215–225. [CrossRef]
  15. T. Nagai, Global existence and decay estimates of solutions to a parabolic-elliptic system of drift-diffusion type in ℝ2. Differential Integral Equations 24 (2011) 29–68. [MathSciNet]
  16. L. Nirenberg, On elliptic partial differential equations. Ann. Scuola Norm. Sup. Pisa 13 (1959) 115–162. [MathSciNet]
  17. A. Raczyński, Weak-Lp solutions for a model of self-gravitating particles with an external potential. Stud. Math. 179 (2007) 199–216. [CrossRef]
  18. D.R. Smart, Fixed Point Theorems. Cambridge University Press, New York (1974).
  19. E.M. Stein, Singular Integrals and Differentiability Properties of Functions. Princeton University Press, Princeton (1970).
  20. G. Wolansky, On steady distributions of self-attracting clusters under friction and fluctuations, Arch. Rational Mech. Anal. 119 (1992) 355–391. [CrossRef] [MathSciNet]
  21. W.P. Ziemer, Weakly Differentiable Functions. Springer-Verlag, New York (1989).

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