I have a question about Spaces involving time from Evans' PDE book.
Let $u \in L^2(0,T; H^1_0(U))$, with $u' \in L^2(0,T; H^{-1}(U))$.
Could we show that $(u_\epsilon)' \to u'$ in $ L^2(0,T; H^{-1}(U))$, where $u_\epsilon = u *\eta_{\epsilon}$ and $\eta_\epsilon$ is a mollifer. Any help would be very much appreciated!