On a damped nonlinear beam equation

2021/03/01 by David Raske, Raske, David
Engineering · Mathematics · #35L76 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical methods for differential equations #Primary 35L35 #Secondary 35Q99 #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2103.00969

openalex publication_date 2021/03/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note we analyze the large time behavior of solutions to an initial/boundary problem involving a damped nonlinear beam equation. We show that under physically realistic conditions on the nonlinear terms in the equation of motion the energy is a decreasing function of time and solutions converge to a stationary solution with respect to a desirable norm.

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