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Existence of variational solutions to doubly nonlinear systems in nondecreasing domains

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For q ∈ ( 0 , ∞ ) , we consider the Cauchy-Dirichlet problem to doubly nonlinear systems of the form ∂ 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 &#8834... ...