Lukkassen, Dag; Meidell, Annette; Wall, Peter Bounds on the effective behavior of a homogenized generalized Reynolds equation. (English) Zbl 1141.35327 J. Funct. Spaces Appl. 5, No. 2, 133-150 (2007). Summary: We study upper and lower bounds for estimating the effective behavior described by homogenizing a problem of the type \[ {\partial\over\partial x_1}\Biggl(a_1\Biggl(x, {x\over\varepsilon}\Biggr) {\partial u_\varepsilon\over\partial x_1}- b_1\Biggl(x,{x\over \varepsilon}\Biggr)\Biggr)+ {\partial\over\partial x_2}\Biggl(a_2\Biggl(x,{x\over\varepsilon}\Biggr) {\partial u_\varepsilon\over\partial x_2}- b_2\Biggl(x, {x\over\varepsilon}\Biggr)\Biggr)= f(x), \] which is a generalization of the Reynold equation. All cases when these bounds coincide are also found. Cited in 10 Documents MSC: 35B27 Homogenization in context of PDEs; PDEs in media with periodic structure 74Q20 Bounds on effective properties in solid mechanics 35B45 A priori estimates in context of PDEs Keywords:upper and lower bounds PDFBibTeX XMLCite \textit{D. Lukkassen} et al., J. Funct. Spaces Appl. 5, No. 2, 133--150 (2007; Zbl 1141.35327) Full Text: DOI