Periodic waves in unsaturated porous media with hysteresis

TL;DR

This paper proves the existence of time-periodic solutions in a PDE model of unsaturated porous media flow with hysteresis, under small boundary forcing, highlighting the role of hysteresis in such systems.

Contribution

It establishes the existence of time-periodic solutions for a PDE system with hysteresis in porous media, under small boundary forcing conditions.

Findings

Time-periodic solutions exist for small boundary forcing.

Hysteresis effects are incorporated into the PDE model.

Solutions remain within the convexity domain of the hysteresis operator.

Abstract

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 prove that a time periodic response exists as long as the amplitude of the forcing terms is small enough to keep the solution within the convexity domain of the hysteresis operator.