For \(q \in (0, \infty )\) , we consider the Cauchy–Dirichlet problem to doubly nonlinear systems of the form \(\begin{aligned} \partial _t \big ( |u|^{q-1}u \big ) - \operatorname {div} \big ( D_\xi f(x,u,Du) \big ) = - D_u f(x,u,Du) \end{aligned}\) in a bounded noncylindrical domain \(E \subset \mathbb {R}^{n+1}\) . We assume that \(x \mapsto f(x,u,\xi )\) is integrable, that \((u,\xi ) \mapsto f(x,u,\xi )\) is convex, and that f satisfies a p-coercivity condition for some \(p \in (1,\infty )\) . However, we do not impose any specific growth condition from above on f. For nondecreasing domains that merely satisfy \(\mathcal {L}^{n+1}(\partial E) = 0\) , we prove the existence of variational solutions \(u \in C^{0}([0,T];L^{q+1}(E,\mathbb {R}^N))\) via a nonlinear version of the method of minimizing movements. Moreover, under additional assumptions on E and a p-growth condition on f, we show that \(|u|^{q-1}u\) admits a weak time derivative in the dual \((V^{p,0}(E))^{\prime }\) of the subspace \(V^{p,0}(E) \subset L^p(0,T;W^{1,p}(\Omega ,\mathbb {R}^N))\) that encodes zero boundary values.
