Scaling laws and convergence for the advection-diffusion equation

Annals of Applied Probability

Volumn 8, Issue 3, 1998, Pages 649-663

  Gaudron, Guillaume ^a  

^a UNIVERSITÉ DE PROVENCE   (France)

Author keywords

Advection diffusion; Random media; Scaling laws; Stochastic processes

Indexed keywords

EID: 0032222164     PISSN: 10505164     EISSN: None     Source Type: Journal    
DOI: 10.1214/aoap/1028903445     Document Type: Article

References (13)

1. AVELLANEDA, M. (1996). Homogenization and renormalization: the mathematics of multi-scale random media and turbulent diffusion. In Dynamical Systems and Probabilistic methods in PDE. 251-268. Amer. Math. Soc., Providence, RI.
2. AVELLANEDA, M., ELLIOTT, F. and APELIAN, C. (1993). Trapping, percolation, and anomalous diffusion of particles in a two-dimensional random field. J. Statist. Phys. 72 1227-1304.
3. AVELLANEDA, M. and MAJDA, A. (1990). Mathematical models with exact renormalization for turbulent transport. Comm. Math. Phys. 131 381-429.
4. AVELLANEDA, M. and MAJDA, A. (1991). An integral representation and bounds on the effective density in passive advection by laminar and turbulent flows. Comm. Math. Phys. 138 339-391.
5. BATCHELOR, G. K. (1982). The Theory of Homogeneous Turbulence. Cambridge Univ. Press.
6. BILLINGSLEY, P. (1968). Convergence of Probability Measures. Wiley, New York.
7. CARMONA, R. and XU, L. (1998). Renormalization results for time dependent incompressible OU velocity field. Preprint.
8. GAUDRON, G. and PARDOUX, E. (1998). Approche probabiliste de l'homogénéisation pour des EDP semi-linéaires à coefficients aléatoires. Unpublished manuscript.
9. MAJDA, A. (1993). The random uniform shear layer: an explicit example of turbulent diffusion with broad tail probability distributions. Phys. Fluids A 5 1963-1970.
10. McLAUGHLIN, R. M. and MAJDA, A. (1993). The effect of mean flows on enhanced diffusivity in transport by incompressible periodic velocity fields. Stud. Appl. Math. 89 245-279.
11. MATHIEU, P. (1998). Random additive functionals of Brownian motion: the Matheron-de Marsily model. Preprint, LATP.
12. OLLA, S. (1994). Homogenization of diffusion processes in random fields. Cours de l'Ecole Doctorale de l'Ecole Polytechnique.
13. FEDOTOV, S. (1995). Renormalization for reaction-front propagation in a fully developed turbulent shear-flow. Phys. Rev. E 52 3835-3839.