Wednesday, April 21, 2021 — 3:30 pm — online talk
Abstract: Understanding the mechanism of solid-liquid interaction in deformable porous media is the goal of many existing models in the engineering literature. Here we derive a model describing fluid diffusion in an unsaturated deformable porous medium, assuming that the fluid may undergo phase transition and that two sources of hysteresis are observed: the solid itself is subject to irreversible plastic deformations, and the fluid flow exhibits capillary hysteresis, which is explained by the surface tension on the interfaces between water and air.
We will then show how to prove existence of a solution in the isothermal case, when phase transition effects are simulated by introducing a suitable nonlinearity. This “simplified” setting already accounts for many of the difficulties that arise in presence of strongly nonlinear pressure-volume interactions.
Taking advantage of the techniques here developed, in the last part of the talk we will give an idea about how to deal with the full problem.
This is a joint work with Pavel Krejčí.