Existence of variational solutions to doubly nonlinear systems in nondecreasing domains

Abstract For q (0, ) q ∈ (0, ∞), we consider the Cauchy–Dirichlet problem to doubly nonlinear systems of the form aligned ₜ (|u|^q-1u) - div (D_ f (x, u, Du) ) = - Dᵤ f (x, u, Du) aligned ∂ t (| u | q - 1 u) - div (D ξ f (x, u, D u) ) = - D u f (x, u, D u) in a bounded noncylindrical domain E R^n+1 E ⊂ R n + 1. We assume that x f (x, u, ) x ↦ f (x, u, ξ) is integrable, that (u, ) f (x, u, ) (u, ξ) ↦ f (x, u, ξ) is convex, and that f satisfies a p -coercivity condition for some p (1, ) p ∈ (1, ∞). However, we do not impose any specific growth condition from above on f. For nondecreasing domains that merely satisfy L^n+1 (E) = 0 L