arXiv subjects

Abdelhakim Dahmani

Publications and source records attributed to Abdelhakim Dahmani.

2 recordsLinked to original sources

arXiv2026

Well-posedness and passivity for a class of bilinear control systems

We study an abstract class of bilinear infinite-dimensional systems that arises in various applications, including district heating systems and quantum control. First, we analyze the existence of mild and classical solutions for abstract bilinear systems with admissible input operators in Banach spaces and study continuous dependence on the data. When the underlying space is a Hilbert space, these results are used to show passivity for a suitably defined co-located output and for mild solutions. The results are applied to the bilinear Schrödinger equation, the Fokker--Planck equation, and a district heating or cooling pipe.

math.AP↗

arXiv2025

One dimensional wave equation with in-domain localized damping and Wentzell boundary conditions

This paper is devoted to the exponential stability for one-dimensional linear wave equations with in-domain localized damping and several types of Wentzell (or dynamic) boundary conditions. In a quite general boundary setting, we establish the exponential decay of solutions towards the corresponding steady states. The results are obtained either by the multiplier method or spectral analysis in an $L^2$-functional framework, and then with input-to-state technics in an $L^p$-functional framework for $p \in (2,\infty)$.

math.AP↗