Work

On multiplicative time-dependent perturbations of semigroups and cosine families generators

Year: 2024

Type: article

Abstract: In this work we aim to investigate a second order PDE modelling a vibrating string. Our strategy consists in transforming the PDE problem into a semilinear second order ODE in a suitable infinite dimensional space. Since the tension coefficient of the PDE may vary with time, the linear operator of the ODE depends on time. We therefore provide sufficient conditions guaranteeing that a suitable family of unbounded linear operators generates a fundamental system.

Source: Discrete and Continuous Dynamical Systems - S

DOI: 10.3934/dcdss.2024154

Authors: Erica Ipocoana, Valentina Taddei

Institution: University of Modena and Reggio Emilia

Language: English

Topic: Stability and Controllability of Differential Equations

Subfield: Control and Systems Engineering

Field: Engineering

Domain: Physical Sciences

Open Access status: diamond

Funders: Istituto Nazionale di Alta Matematica "Francesco Severi", Ministero dell’Istruzione, dell’Università e della Ricerca

Awards: G1162133770, G6676218734, G924608660