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A compactness result for non-periodic structures and its application to homogenization of diffusion-convection equations

Abstract:

The paper proves the strong compactness of the sequence {˜(-, )} in L2(Ω), Ω= Ω×(0, ), Ω ⊂ R3, bounded in the space W1,0 {︁ 2 (Ω) with the sequence of time derivatives ((-, , - ) ˜(-,) )︀}︁ bounded in the space L2 (︀ (0, );W−1 2 (Ω) ) , where characteristic function (-, ) is 1-periodic in a variable ∈ = (︂ − 1 2 , 1 2 )︂3 ⊂ R3. As an application we consider the homogenization of a diffusion-convection equation in nonperiodic structure, given by 1-periodic in characteristic function (-,) with a sequence of divergent-free velocities {(-,)} weakly convergent in L2(Ω).