*Preprint*

**Inserted:** 8 apr 2003

**Last Updated:** 21 nov 2003

**Year:** 2003

**Abstract:**

We study the asymptotic behaviour of a sequence of strongly degenerate parabolic equations $\partial_t (r_h u) - {\rm div}(a \cdot Du)$ with $r_h(x,t) \mau 0$, $r_h \in L^{\infty}(\Om \times (0,T))$. This leads to study, as particular cases, $G$-convergence for elliptic operators ($r_h \equiv 0$), $G$-convergence for parabolic operators ($r_h \equiv 1$), singular perturbations of an elliptic operator ($a_h \equiv a$ and $r_h \to r$, possibly $r\equiv0$).

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