What does $ div_xf $ denote?

Question

I was reading something. then I came across this equation, \begin{equation} \ u_t= a\Delta u+div_x f+h, \ ~~\ \end{equation} and stumbled across this notation $ div_xf $. What does this denotion mean?

Answer 1

If $f: \Bbb R^n \times \Bbb R \to \Bbb R$ then $\mathrm{div}_x f(x,t) = \nabla_x \cdot f = \partial_{x_1}f(x,t) + \dots + \partial_{x_n}f(x,t) $, is the divergence operator with respect to $x = (x_1, \dots, x_n)$, i.e. the sum of the first partial derivatives w.r.t. $x_1, \dots, x_n$.