Asymptotic behavior of the solution of quasilinear parametric variational inequalities in a beam with a thin neck

TL;DR

This paper investigates how solutions to quasilinear parametric variational inequalities behave asymptotically in a cylindrical domain with a thin neck, deriving the corresponding limit problem as the neck becomes vanishingly thin.

Contribution

It provides a rigorous analysis of the asymptotic behavior and derives the limit problem for variational inequalities in a domain with a thin neck, extending existing theories.

Findings

Derived the limit problem for the variational inequalities as the neck thickness tends to zero.

Established the asymptotic behavior of solutions in the thin-neck domain.

Provided mathematical framework for analyzing similar problems in thin structures.

Abstract

In this paper we study the asymptotic behavior of the solution of quasilinear parametric variational inequalities posed in a cylinder with a thin neck, and we obtain the limit problem.