Nonlinear Partial Differential Equations

Date: March 19, 2024

Time: 3:00PM - 4:00PM

Location: BLOC 302

Speaker: Marita Thomas, Freie Universitaet - Berlin

Title: Analysis of a model for visco-elastoplastic two-phase flows in geodynamics

Abstract: A model for an incompressible fluid of both viscoelastic and viscoplastic behavior is revisited, which is used in geodynamics, e.g., to describe the evolution of fault systems in the lithosphere on geological time scales. The Cauchy stress of this fluid is composed of a viscoelastic Stokes-like contribution and of an additional internal stress. The model thus couples the momentum balance with the evolution law of this extra stress, which features the Zaremba-Jaumann time-derivative and a non-smooth viscoplastic dissipation mechanism. This model is augmented to the situation of a bi-phasic material that undergoes phase separation according to a Cahn-Hilliard-type evolution law. Suitable concepts of weak solutions are discussed for the coupled model. This is joint work with Fan Cheng (FU Berlin) and Robert Lasarzik (WIAS and FU Berlin) within project C09 'Dynamics of rock dehydration on multiple scales' of CRC 1114 'Scaling Cascades in Complex Systems' funded by the German Research Foundation.