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Homogenization of a Nonlinear Convection‐Diffusion Equation with Rapidly Oscillating Coefficients and Strong Convection
Author(s) -
Marušić-Paloka Eduard,
Piatnitski Andrey L.
Publication year - 2005
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610705006824
Subject(s) - homogenization (climate) , convection–diffusion equation , convection , nonlinear system , mathematical analysis , diffusion equation , mathematics , cauchy distribution , physics , mechanics , biodiversity , ecology , quantum mechanics , economics , biology , service (business) , economy
A Cauchy problem for a nonlinear convection‐diffusion equation with periodic rapidly oscillating coefficients is studied. Under the assumption that the convection term is large, it is proved that the limit (homogenized) equation is a nonlinear diffusion equation which shows dispersion effects. The convergence of the homogenization procedure is justified by using a new version of a two‐scale convergence technique adapted to rapidly moving coordinates.