Geodesic
Homogenization of a~random non-stationary convection-diffusion problem
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 57 (2002) no. 4, pp. 729-751

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The homogenization problem is studied for a non-stationary convection-diffusion equation with rapidly oscillating coefficients periodic in the spatial variables and stationary random in the time. Under the assumption that the coefficients of the equation have rather good mixing properties, it is shown that, in properly chosen moving coordinates, the distribution of the solution of the original problem converges to the solution of the limit stochastic partial differential equation. The homogenized problem is well-posed and determines the limit measure uniquely. 
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     author = {M. L. Kleptsyna and A. L. Piatnitski},
     title = {Homogenization of a~random non-stationary convection-diffusion problem},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {729--751},
     publisher = {mathdoc},
     volume = {57},
     number = {4},
     year = {2002},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/RM_2002_57_4_a3/}
}
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M. L. Kleptsyna; A. L. Piatnitski. Homogenization of a~random non-stationary convection-diffusion problem. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 57 (2002) no. 4, pp. 729-751. http://geodesic.mathdoc.fr/item/RM_2002_57_4_a3/