A new partial differential nonlinear system containing quasivariational and parabolic variational inequalities and its application

TL;DR

This paper introduces a novel nonlinear PDE system with variational inequalities, proves its unique solvability, and applies it to complex contact problems involving memory effects and material wear.

Contribution

It presents the first analysis of a coupled PDE and variational inequalities system with applications to viscoelastic contact problems.

Findings

Proved unique solvability of the system using Banach's fixed point theorem.

Applied the theoretical results to real-world contact problems with memory effects.

Demonstrated the model's relevance to wear and damage phenomena in materials.

Abstract

We study a new nonlinear system which contains a partial differential equation, a quasivariational inequality and a parabolic variational inequality in Banach spaces. We obtain the unique solvability of the coupled system under moderate conditions by using the Banach's fixed point theorem. We employ the main results to investigate a viscoelastic frictional contact problem with long-memory effects, wear processes, and damage phenomenon.