Stress-diffusive regularizations of non-dissipative rate-type materials - Burczak, Jan; Málek, Josef; Minakowski, Piotr (Discrete and continuous dynamical systems, 2017)
We consider non-dissipative (elastic) rate-type material models that are derived within the Gibbs-potential-based thermodynamic framework. Since the absence of any dissipative mechanism in the model prevents us from establishing even a local-in-time existence result in two spatial dimensions for a spatially periodic problem, we propose two regularisations. For such regularized problems we obtain well-posedness of the planar, spatially periodic problem. In contrast with existing results, we prove ours for a regularizing term present solely in the evolution equation for the stress.
Revised February 2017
Gesehen am 08.06.2018