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Ricardo Andrade
Ricardo Andrade
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(Crossposted from MSE due to no replies)

I'm trying to understand the proof that (c) implies (a) here in the following proposition (here, $\mathcal{V} = L^2(0,T;V)$). See the very last line in the image for that part: $$$$

​

enter image description here $$$$ I

​

I give here Proposition 1.1 which the proof uses. $$$$

​

enter image description here

I do not understand how it's used in the proof. I'd appreciate an explanation. Thank you.

Here, $$W_2(0,T) = \{u \in \mathcal V : u' \in \mathcal V'\}$$$$ W_2(0,T) = \{u \in \mathcal V : u' \in \mathcal V'\} $$ and enter image description here

(All images cut from Showalter's book Monotone Operators in Banach Space)

(Crossposted from MSE due to no replies)

I'm trying to understand the proof that (c) implies (a) here in the following proposition (here, $\mathcal{V} = L^2(0,T;V)$). See the very last line in the image for that part: $$$$

enter image description here $$$$ I give here Proposition 1.1 which the proof uses. $$$$ enter image description here

I do not understand how it's used in the proof. I'd appreciate an explanation. Thank you.

Here, $$W_2(0,T) = \{u \in \mathcal V : u' \in \mathcal V'\}$$ and enter image description here

(All images cut from Showalter's book Monotone Operators in Banach Space)

(Crossposted from MSE due to no replies)

I'm trying to understand the proof that (c) implies (a) here in the following proposition (here, $\mathcal{V} = L^2(0,T;V)$). See the very last line in the image for that part:

​

enter image description here

​

I give here Proposition 1.1 which the proof uses.

​

enter image description here

I do not understand how it's used in the proof. I'd appreciate an explanation. Thank you.

Here, $$ W_2(0,T) = \{u \in \mathcal V : u' \in \mathcal V'\} $$ and enter image description here

(All images cut from Showalter's book Monotone Operators in Banach Space)

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Don't understand proof of equivalence Two equivalent definitions of weak solutionssolution to parabolic PDEPDE; don't understand proof

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Don't understand proof of equivalence of weak solutions to parabolic PDE

(Crossposted from MSE due to no replies)

I'm trying to understand the proof that (c) implies (a) here in the following proposition (here, $\mathcal{V} = L^2(0,T;V)$). See the very last line in the image for that part: $$$$

enter image description here $$$$ I give here Proposition 1.1 which the proof uses. $$$$ enter image description here

I do not understand how it's used in the proof. I'd appreciate an explanation. Thank you.

Here, $$W_2(0,T) = \{u \in \mathcal V : u' \in \mathcal V'\}$$ and enter image description here

(All images cut from Showalter's book Monotone Operators in Banach Space)