# Analysis of nonlinear poroviscoelastic flows with discontinuous porosities

## TL;DR

This paper investigates the mathematical properties of nonlinear poroviscoelastic flows in porous media, focusing on existence, uniqueness, and well-posedness when porosity functions are discontinuous, including cases with porosity waves.

## Contribution

It establishes conditions for the existence and uniqueness of solutions in models with nonsmooth porosities, advancing understanding of flow behavior with discontinuous porosity profiles.

## Key findings

- Proved well-posedness for flows with jump discontinuities in porosity.
- Identified conditions leading to porosity waves.
- Analyzed nonlinear interactions between porosity and pressure.

## Abstract

Existence and uniqueness of solutions is shown for a class of viscoelastic flows in porous media with particular attention to problems with nonsmooth porosities. The considered models are formulated in terms of the time-dependent nonlinear interaction between porosity and effective pressure, which in certain cases leads to porosity waves. In particular, conditions for well-posedness in the presence of initial porosities with jump discontinuities are identified.