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We study the connection between mild and weak solutions for a class ofmeasure-valued evolution equations on the bounded domain $[0,1]$. Mass moves,driven by a velocity field that is either a function of the spatial variableonly, $v=v(x)$, or depends on the solution $\mu$ itself: $v=v[\mu](x)$. Theflow is stopped at the boundaries of $[0,1]$, while mass is gated away by acertain right-hand side. In previous works [J. Differential Equations, 259(2015), pp. 1068-1097] and [SIAM J. Math. Anal., 48 (2016), pp. 1929-1953], weshowed the existence and uniqueness of appropriately defined mild solutions for$v=v(x)$ and $v=v[\mu](x)$, respectively. In the current paper we define weaksolutions (by specifying the weak formulation and the space of test functions).The main result is that the aforementioned mild solutions are weak solutions,both when $v=v(x)$ and when $v=v[\mu](x)$.

Mild solutions are weak solutions in a class of (non)linear measure-valued evolution equations on a bounded domain