Dynamical poroplasticity model – Existence theory for gradient type nonlinearities with Lipschitz perturbations

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In this article we study existence theory to a non-coercive fully dynamic model of poroplasticity with the non-homogeneous boundary conditions where the constitutive function is a continuous element of class LM (it is a sum of a maximal monotone map G and a globally Lipschitz map l). Without any additional growth conditions we are able to prove the existence of a solution such that the inelastic constitutive equation is satisfied in the measure-valued sense. Moreover, if G is a gradient of a differentiable convex function, then there exists a solution such that the constitutive equation is satisfied almost everywhere.