Weak solutions for nonlinear waves in adhesive phenomena

TL;DR

This paper introduces a framework for weak solutions to a semilinear wave equation modeling adhesive interactions between elastic bodies and substrates, accommodating vector-valued cases and non-local operators like fractional Laplacians.

Contribution

It extends the concept of weak solutions to complex, multi-dimensional, and non-local wave equations in adhesive phenomena.

Findings

Established a notion of weak solutions for complex wave models

Included vector-valued and non-local operator cases

Built on and extended previous results in the field

Abstract

We discuss a notion of weak solution for a semilinear wave equation that models the interaction of an elastic body with a rigid substrate through an adhesive layer, relying on results in [2]. Our analysis embraces the vector-valued case in arbitrary dimension as well as the case of non-local operators (e.g. fractional Laplacian).