{"ID":2874665,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.04275","arxiv_id":"2509.04275","title":"Polynomial Stability of Non-Linearly Damped Contraction Semigroups","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.","short_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 abstr...","url_abs":"https://arxiv.org/abs/2509.04275","url_pdf":"https://arxiv.org/pdf/2509.04275v2","authors":"[\"Lassi Paunonen\",\"David Seifert\"]","published":"2025-09-04T14:50:37Z","proceeding":"math.FA","tasks":"[\"math.FA\",\"math.AP\",\"math.OC\"]","methods":"[]","has_code":false}