The Preisach model is a well-known model of hysteresis in the modern nonlinear science.
This paper provides an overview of works that are focusing on the study of dynamical …

We consider a scalar conservation law with hysteresis in which the flux function depends on
the history of the evolution. The work is motivated by the need to account for hysteresis in …

A PDE system consisting of the momentum balance, mass balance, and energy balance
equations for displacement, capillary pressure, and temperature as a model for unsaturated …

A PDE system consisting of the mechanical equilibrium and mass balance equations for
displacement and capillary pressure as a model for fluid diffusion in a partially saturated …

We propose to model the lungs as a viscoelastic deformable porous medium with a
hysteretic pressure–volume relationship described by the Preisach operator. Breathing is …

In this paper, a continuum model is introduced for fluid flow in a deformable porous medium,
where the fluid may undergo phase transitions. Typically, such problems arise in modeling …

We consider a PDE system with degenerate hysteresis describing unsaturated flow in 3D
porous media. Assuming that a time periodic forcing is prescribed on the boundary, we …

The full quasistatic thermomechanical system of PDEs, describing water diffusion with the
possibility of freezing and melting in a visco-elasto-plastic porous solid, is studied in detail …

We propose a model for multicomponent flow of immiscible fluids in a deformable porous
medium accounting for capillary hysteresis. Oil, water, and air in the soil pores offer a typical …

We propose a mathematical model describing the process of filling the pores of a building
material with lime water solution with the goal to improve the consistency of the porous solid …