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Where can I find a proof that $\mathcal{D}(0,T;V)$ (the space of $V$-valued compactly supported functions on $[0,T]$) is dense in the space $W(0,T)$, where $$W(0,T) = \{ u \in L^2(0,T;V) : u' \in L^2(0,T;V^*)\},$$$$W(0,T) := \{ u \in L^2(0,T;V) : u' \in L^2(0,T;V^*)\},$$ where $V$ is Hilbert\Banach? I need the proof in the English language.

Where can I find a proof that $\mathcal{D}(0,T;V)$ is dense in the space $W(0,T)$, where $$W(0,T) = \{ u \in L^2(0,T;V) : u' \in L^2(0,T;V^*)\},$$ where $V$ is Hilbert\Banach? I need the proof in the English language.

Where can I find a proof that $\mathcal{D}(0,T;V)$ (the space of $V$-valued compactly supported functions on $[0,T]$) is dense in the space $W(0,T)$, where $$W(0,T) := \{ u \in L^2(0,T;V) : u' \in L^2(0,T;V^*)\},$$ where $V$ is Hilbert\Banach? I need the proof in the English language.

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  • 113
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$\mathcal{D}(0,T;V)$ is dense in $W(0,T)$

Where can I find a proof that $\mathcal{D}(0,T;V)$ is dense in the space $W(0,T)$, where $$W(0,T) = \{ u \in L^2(0,T;V) : u' \in L^2(0,T;V^*)\},$$ where $V$ is Hilbert\Banach? I need the proof in the English language.