Asymptotic for a second order evolution equation with vanishing damping term and Tikhonov regularization

TL;DR

This paper studies the long-term behavior of solutions to a second order differential equation that includes a diminishing damping effect, a convex potential, and Tikhonov regularization, revealing their asymptotic properties.

Contribution

It provides new insights into the asymptotic analysis of second order evolution equations with vanishing damping and Tikhonov regularization.

Findings

Characterization of asymptotic behavior of solutions

Conditions for convergence to minimizers

Impact of vanishing damping on solution stability

Abstract

We investigate the asymptotic behavior of solutions to a second order differential equation with vanishing damping term, convex potential and regularizing Tikhonov term.