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Results tagged with compactness
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user 16530
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Accepted
A compactness result: if $f_n(u_n) \rightharpoonup w$ in $L^2(0,T;L^2)$, then $f_n(u_n) \to ...
I agree with your edited question.
In fact, the information about $u_n$ seems to be unnecessary.
Consider $g_n := f_n(u_n)$; then your assumptions give
$g_n\rightharpoonup w$ in $L^2(0,T;L^2)$ …
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