# Nonmonotone slip problem for miscible liquids

## TL;DR

This paper establishes the existence and uniqueness of solutions for a complex two-dimensional model of miscible liquids with nonmonotone boundary conditions, using advanced mathematical techniques.

## Contribution

It introduces a novel approach combining regularized Galerkin methods with hemivariational inequalities to handle nonsmooth, multivalued boundary conditions.

## Key findings

- Proves existence of solutions for the nonstationary system.
- Establishes uniqueness of solutions under given conditions.
- Develops a mathematical framework for nonmonotone boundary problems.

## Abstract

In this paper we prove the existence and uniqueness of a solution to the nonstationary two dimensional system of equations describing miscible liquids with nonsmooth, multivalued and nonmonotone boundary conditions of subdifferential type. We employ the regularized Galerkin method combined with results from the theory of hemivariational inequalities.