Hamilton-Jacobi-Bellman equation for optimal control

Chameleon

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May 29, 2022
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Hello!

Could somebody please help me understand, where shall I begin solve this problem?
I mean, I would have known steps if first order conditions where provided for HJB and solution would be, for example, of form V(X)=a+bX, but in this case it's V(C) and what taking partial derivative would give me?Handwritten_2022-05-29_200114.jpg
 
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