arXiv subjects

Rachid Assel

Publications and source records attributed to Rachid Assel.

2 recordsLinked to original sources

arXiv2024

Spectral analysis and best decay rate of the wave propagator on the tadpole graph

We consider the damped wave semigroup on the tadpole graph ${\mathcal R}$. We first give a meticulous spectral analysis, followed by a judicious decomposition of the resolvent's kernel. As a consequence, and by showing that the generalized eigenfunctions form a Riesz basis of some subspace of the energy space $\mathcal{H}$, we establish the exponential decay of the corresponding energy, with the optimal decay rate dictated by the spectral abscissa of the relevant operator.

math.AP↗

arXiv2021

Spectral analysis and stabilization of the dissipative Schrödinger operator on the tadpole graph

We consider the damped Schrödinger semigroup $e^{-it \frac{d^2}{dx^2}}$ on the tadpole graph ${\mathcal R}$. We first give a careful spectral analysis and an appropriate decomposition of the kernel of the resolvent. As a consequence and by showing that the generalized eigenfunctions form a Riesz basis of some subspace of $L^2({\mathcal R})$, we prove that the corresponding energy decay exponentially.

math.AP↗