On large time asymptotics for drift-diffusion-Poisson systems

Transport Theory and Statistical Physics

Volumn 29, Issue 3-5, 2000, Pages 571-581

  Arnold, Anton ^a   Markowich, Peter ^b   Toscani, Giuseppe ^c  

^a TECHNISCHE UNIVERSITÄT BERLIN   (Germany)

^b JOHANNES KEPLER UNIVERSITY LINZ   (Austria)

^c UNIVERSITY OF PAVIA   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034383060     PISSN: 00411450     EISSN: None     Source Type: Journal    
DOI: 10.1080/00411450008205893     Document Type: Article

References (15)

1. A. Arnold, L. Bonilla, P. Markowich, Liapunov functional and large-time asymptotics of mean-field Fokker-Planck equations. Transp. Theo. Stat. Phys. 25(7):733-751, 1996.
2. A. Arnold, P. Markowich, G. Toscani, A. Unterreiter, On logarithmic Sobolev inequalities, Csiszár-Kullback inequalities, and the rate of convergence to equilibrium for Fokker-Planck type equations, preprint, 1998.
3. 1-decay of solutions of the porous medium equation to self-similarity, to appear in Ind. Univ. J. Math., 1999.
4. I. Csiszár, Eine informationstheoretische Ungleichung und ihre Anwendung auf den Beweis von Markoffschen Ketten, Magyar Tud. Akad. Mat. Kutató Int. Közl., 8:85-108, 1963.
5. 3 AS, 1(2):183-208, 1991.
6. J. Dolbeault, M. del Pino, Generalized Sobolev inequalities and asymptotic behaviour in fast diffusion and porous medium problems, submitted to Proc. Roy. Society of Edinburgh, Preprint Ceremade, 1999.
7. E.B. Fabes, D.W. Stroock, A new Proof of Moser's Parabolic Harneck Inequality using the old Idea of Nash, Arch. Rat. Mech. Anal., Vol. 96, 327-338, 1986.
8. H. Gajewski, On Existence, Uniqueness, and Asymptotic Behaviour of Solutions of the Basic Equations for Carrier Transport in Semiconductors, ZAMM, 65(2):101-108, 1985.
9. L. Gross, Logarithmic Sobolev Inequalities and Contractivity Properties of Semigroups, Lecture Notes in Mathematics 1563, E. Fabes et al. (Eds.) "Dirichlet Forms", Springer Berlin-Heidelberg, 1993.
10. R. Holley and D. Stroock, Logarithmic Sobolev Inequalities and Stochastic Ising Models, J. Stat. Phys. 46 (5&6):1159-1194, 1987.
11. S. Kullback, Information Theory and Statistics, John Wiley, 1959.
12. J.W. Jerome, Analysis of Charge Transport - A Mathematical Study of Semiconductor Devices, Springer, Berlin-Heidelberg-New York, 1996
13. P.A. Markowich, C.A. Ringhofer, C. Schmeiser, Semiconductor Equations, Springer, New York, 1990.
14. J. Nash, Continuity of solutions of parabolic and elliptic equations. Amer. J. Math. 80:931-954, 1958.
15. G. Toscani, Kinetic approach to the asymptotic behaviour of the solution to diffusion equations, Rend. di Matematica, 16:329-346. 1996.