arXiv subjects

S. Nicaise

Publications and source records attributed to S. Nicaise.

5 recordsLinked to original sources

arXiv2025

Journey Through the World of Dynamical Systems on Networks

We present a subjective selection of methods for complex systems analysis ranging from statistical tools through numerical methods based on AI to both linear and non-linear ODEs and PDEs. All the notions apply the network structure and are presented in the context of applied problems to visualise the strengths and drawbacks of the approach. The major aim of capturing such a broad overview is to understand the interrelations between network theories that seem to be distant from the mathematical perspective.

math.DS↗

arXiv2024

Frequency-explicit stability estimates for time-harmonic elastodynamic problems in nearly incompressible materials

We consider time-harmonic elastodynamic problems in heterogeneous media.cWe focus on scattering problems in the high-frequency regime and incnearly incompressible media, where the the angular frequency $ω$ and ratio of the Lamé parameters $λ/μ$ may both be large. We derive stability estimates controlling the norm of the solution by the norm of the right-hand side up to a fully-explicit constant. Crucially, under natural assumptions on the domain and coefficients, this constant increases linearly with $ω$ and is uniform in the ratio $λ/μ$.

math.AP↗

arXiv2012

Polynomial stabilization of some dissipative hyperbolic systems

We study the problem of stabilization for the acoustic system with a spatially distributed damping. Imposing various hypotheses on the structural properties of the damping term, we identify either exponential or polynomial decay of solutions with growing time. Expo- nential decay rate is shown by means of a time domain approach, reducing the problem to an observability inequality to be verified for solutions of the associated conservative problem. In addition, we show a polynomial stabilization result, where the proof uses a frequency domain method and combines a contradiction argument with the multiplier technique to carry out a special analysis for the resolvent.

math.AP↗

arXiv2010

Stabilization of a piezoelectric system

We consider a stabilization problem for a piezoelectric system. We prove an exponential stability result under some Lions geometric condition. Our method is based on an identity with multipliers that allows to show an appropriate observability estimate.

math.AP↗

arXiv2010

Feedback boundary stabilization of wave equations with interior delay

In this paper we consider a boundary stabilization problem for the wave equation with interior delay. We prove an exponential stability result under some Lions geometric condition. The proof of the main result is based on an identity with multipliers that allows to obtain a uniform decay estimate for a suitable Lyapunov functional.

math.AP↗