Considering the semilinear differential inclusion \(\frac{du}{dt}(t) \in A u(t) + F(u(t))\) where \(A\) is the generator of a semigroup and \(F\) is a nonempty, closed convex and bounded set-valued map, the authors investigate the existence of mild solutions viable in a given closed set \(D\). They prove that, when \(F\) is locally weakly-weakly upper semi-continuous, a weak sequential tangency condition is a necessary and sufficient condition in order that \(D\) be a viable domain.