Abstract:
An initial-boundary-value problem is considered for the parabolic equation
$$
\Phi^\varepsilon(x)u^\varepsilon_t-\operatorname{div}(A^\varepsilon(x)
\nabla u^\varepsilon)=f^\varepsilon(x), \qquad x\in\Omega, \quad t>0,
$$
with discontinuous diffusion tensor
$A^\varepsilon(x)$.
This tensor is assumed to degenerate as $\varepsilon\to0$ in the whole of the domain
$\Omega$ except on a set ${\mathscr F}^{(\varepsilon)}$ of asymptotically small measure.
It is shown that the behaviour of the solutions $u^\varepsilon$ as $\varepsilon\to0$
is described by a homogenized model with memory.
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