# Global existence for a nonlocal model for adhesive contact

## TL;DR

This paper proves the global-in-time existence of solutions for a complex nonlocal PDE model describing adhesive contact with damage and elongation effects, advancing the mathematical understanding of such contact problems.

## Contribution

It introduces a novel analytical approach to establish global existence for a nonlinear nonlocal PDE system modeling adhesive contact with damage.

## Key findings

- Global existence of solutions established
- Handles complex nonlinearities and nonlocal damage effects
- Extends local solutions to global solutions using a nonstandard method

## Abstract

In this paper we address the analytical investigation of a model for adhesive contact, which includes nonlocal sources of damage on the contact surface, such as the elongation. The resulting PDE system features various nonlinearities rendering the unilateral contact conditions, the physical constraints on the internal variables, as well as the integral contributions related to the nonlocal forces. For the associated initial-boundary value problem we obtain a global-in-time existence result by proving the existence of a local solution via a suitable approximation procedure and then by extending the local solution to a global one by a nonstandard prolongation argument.