Work

Polynomial stability of non-linearly damped contraction semigroups

Year: 2026

Type: article

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.

Source: Journal of Differential Equations

DOI: 10.1016/j.jde.2026.114129

Authors: Lassi Paunonen, David Seifert

Institutions: Tampere University, University of Tampere, Newcastle University

Language: English

Topic: Stability and Controllability of Differential Equations

Subfield: Control and Systems Engineering

Field: Engineering

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,550

Funders: Academy of Finland, Luonnontieteiden ja Tekniikan Tutkimuksen Toimikunta, Heilbronn Institute for Mathematical Research