Homogenization of forward‐backward parabolic equations

We study the homogenization of the equation $\[R(\varepsilon ^{-1}x)\frac{ \curpartial u_{\varepsilon }}{\curpartial t}-\Delta u_{\varepsilon }=f,\]$ where R is a periodic function which may vanish or change sign, with appropriate initial/final conditions. The main tool is a compactness result for sequences of functions which have bounded norms in the spaces associated to the problems.