TY - GEN A1 - Knees, Dorothee A1 - Rossi, Riccarda A1 - Zanini, Chiara T1 - A quasilinear differential inclusion for viscous and rate-independent damage systems in non-smooth domains N2 - This paper focuses on rate-independent damage in elastic bodies. Since the driving energy is nonconvex, solutions may have jumps as a function of time, and in this situation it is known that the classical concept of energetic solutions for rate-independent systems may fail to accurately describe the behavior of the system at jumps. Therefore, we resort to the (by now well-established) vanishing viscosity approach to rate-independent modeling and approximate the model by its viscous regularization. In fact, the analysis of the latter PDE system presents remarkable difficulties, due to its highly nonlinear character. We tackle it by combining a variational approach to a class of abstract doubly nonlinear evolution equations, with careful regularity estimates tailored to this specific system relying on a q-Laplacian type gradient regularization of the damage variable. Hence, for the viscous problem we conclude the existence of weak solutions satisfying a suitable energy-dissipation inequality that is the starting point for the vanishing viscosity analysis. The latter leads to the notion of (weak) parameterized solution to our rate-independent system, which encompasses the influence of viscosity in the description of the jump regime. KW - rate-independent damage evolution KW - vanishing viscosity method KW - arclenght reparameterization KW - time discretization KW - regularity estimates Y1 - 2014 UR - https://opus4.kobv.de/opus4-matheon/frontdoor/index/index/docId/1260 UR - https://nbn-resolving.org/urn:nbn:de:0296-matheon-12605 ER -