A linear homogenization problem with time dependent coefficient
Maria Luisa Mascarenhas · Transactions of the American Mathematical Society · 1984
We consider: the homogenization problem \[ { ( ∂ u ε / ∂ t ) ( x , t ) + β ε ( x ) u ε ( x , t ) = 0 , a m p ; t ⩽ 0 , u ε ( x , 0 ) = ϕ ( x ) , \begin {cases} (\partial u\varepsilon /\partial t)(x,t) + \beta _\varepsilon (x) u_\varepsilon (x,t) = 0, & t\leqslant 0, \\ u_\varepsilon (x,0) = \phi (x), \end {cases} \] where β \beta is a strictly positive bounded real function, periodic of period 1 1 , and β ε ( x ) = β ( x / ε ) {\beta _\varepsilon }(x) = \beta (x/\varepsilon ) ; the equivalent integral equation \[