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arXiv · 2509.04275

Polynomial Stability of Non-Linearly Damped Contraction Semigroups

Lassi Paunonen·David Seifert
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Abstract

We investigate the stability properties of an abstract class of semi-linear systems. Our main result establishes rational rates of decay for classical solutions assuming a certain non-uniform observability estimate for the linear part and suitable conditions on the non-linearity. We illustrate the strength of our abstract results by applying them to a one-dimensional wave equation with weak non-linear damping and to an Euler-Bernoulli beam with a tip mass subject to non-linear damping.

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Lassi Paunonen, David Seifert. 2025-09-04. Polynomial Stability of Non-Linearly Damped Contraction Semigroups. https://doi.org/10.1016/j.jde.2026.114129

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