I have recently started reading some calculus of variations/PDE stuff, not having done this for absolutely ages i'm struggling with notation. (if anyone has a good reference for calculus of variations/PDE/ multi-variable calculus just to re familiarise with all the basics it would be great).
My question :
In what i'm reading the author has a PDE $$\partial_t\rho_t=\text{div}(\rho_t \nabla F'(\rho_t)), $$
where $\rho_t : \mathbb{R}^d\to\mathbb{R}$ for each $t\in[0,\infty)$, and $$F(\rho_t):=\int v(x)\rho_t(x)dx+\int u(\rho_t(x))dx, $$ for some functions $v:\mathbb{R}^d\to \mathbb{R}$, $u:\mathbb{R}\to \mathbb{R}$. Can anyone explain the notation $\nabla F'(\rho_t)$, is $'$ a transpose? how can we take $\nabla$ of a functional...