Large time behavior of solutions to nonlinear beam equations

TL;DR

This paper studies the long-term behavior of solutions to nonlinear damped beam equations, demonstrating that their energies decay exponentially over time, which provides insights into the stability of such systems.

Contribution

It establishes exponential energy decay for solutions to a specific class of nonlinear damped beam equations, advancing understanding of their stability properties.

Findings

Solutions' energies decay exponentially over time

Global pseudo classical solutions exist for the problem

Provides stability analysis for nonlinear beam equations

Abstract

In this article we will investigate the large time behavior of solutions of a special class of initial/boundary value problems that involve nonlinear damped beam equations. We will show that the solution energies of global pseudo classical solutions to these initial/boundary value problems decay exponentially.