Abstract:
A complete asymptotic expansion is constructed for a second-order equation of elliptic type with a small parameter in the highest-order derivative and rapidly oscillating coefficients.
Bibliography: 11 titles.
Citation:
A. L. Piatnitski, “Averaging a singularly perturbed equation with rapidly oscillating coefficients in a layer”, Math. USSR-Sb., 49:1 (1984), 19–40
This publication is cited in the following 12 articles:
Irina Pettersson, Andrey Piatnitski, “Stationary convection–diffusion equation in an infinite cylinder”, Journal of Differential Equations, 264:7 (2018), 4456
V. V. Zhikov, S. E. Pastukhova, “Operator estimates in homogenization theory”, Russian Math. Surveys, 71:3 (2016), 417–511
A. Piatnitski, V. Rybalko, “On the first eigenpair of singularly perturbed operators with oscillating coefficients”, Communications in Partial Differential Equations, 41:1 (2016), 1
G. Allaire, I. Pankratova, A. Piatnitski, “Homogenization of a nonstationary convection-diffusion equation in a thin rod and in a layer”, SeMA, 58:1 (2012), 53
G. Allaire, I. Pankratova, A. Piatnitski, “Homogenization and concentration for a diffusion equation with large convection in a bounded domain”, Journal of Functional Analysis, 2011
Gregoire Allaire, Andro Mikeli, Andrey Piatnitski, “Homogenization Approach to the Dispersion Theory for Reactive Transport through Porous Media”, SIAM J Math Anal, 42:1 (2010), 125
Andro Mikelić, Carole Rosier, “Rigorous upscaling of the infinite adsorption rate reactive flow under dominant Peclet number through a pore”, Ann Univ Ferrara, 53:2 (2007), 333
Andro Mikelić, Vincent Devigne, C. J. van Duijn, “Rigorous Upscaling of the Reactive Flow through a Pore, under Dominant Peclet and Damkohler Numbers”, SIAM J Math Anal, 38:4 (2006), 1262
A. Bourgeat, M. Jurak, A. L. Piatnitski, “Averaging a transport equation with small diffusion and oscillating velocity”, Math Meth Appl Sci, 26:2 (2003), 95
M. L. Kleptsyna, A. L. Piatnitski, “Homogenization of a random non-stationary convection-diffusion problem”, Russian Math. Surveys, 57:4 (2002), 729–751
S. M. Kozlov, A. L. Piatnitski, “Averaging on a background of vanishing viscosity”, Math. USSR-Sb., 70:1 (1991), 241–261
G. V. Sandrakov, “Averaging principles for eguations with rapidly oscillatory coefficients”, Math. USSR-Sb., 68:2 (1991), 503–553
Citation in format AMSBIB
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