Julian Edward

collaborators

5 papers

math.OC2026

Boundary null controllability of weakly coupled structurally damped beams

Julian Edward, Yacouba Simpore

We prove boundary null controllability in any positive time for a finite system of Euler--Bernoulli beams with possibly non-diagonalizable coupling. For $0 < ρ < 2$ , a Fourier--Jordan…

math.AP2026

Null-controllability for the beam equation with structural damping. Part 2: Integration by parts for fractional Laplacians and boundary control

Sergei Avdonin, Julian Edward

Let $Δ$ be the Neumann Laplacian on the interval $(0, π)$ , and let $T > 0$ . An integration by parts formula is proven for the spectral fractional Laplacian, $(- Δ)^{α}$ , for $α \in (0, 1)$ …

math.AP2026

A symmetry formula for the spectral fractional Laplacian, and applications to boundary controllability for plate equation with structural damping

Sergei Avdonin, Julian Edward

Let $Δ$ be the Dirichlet Laplacian on a bounded domain $Ω \subset R^{N}$ , and let $(- Δ)^{α}$ be the associated spectral fractional Laplacian with $α \leq 1, ρ < 2$ . For genera…

math.OC2026

Boundary null-controllability for the beam equation with classical structural damping

Sergei Avdonin, Julian Edward

Let $Δ$ be the Dirichlet Laplacian on the interval $(0, π)$ , and let $T > 0$ . We prove a well-posedness results for the structurally damped beam equation $$u_{tt}+Δ^2 u-ρΔu_t=0, x\in…

math.AP2025

An inverse problem on a metric graph with cycle

Sergei Avdonin, Julian Edward

Consider a quantum graph consisting of a ring with two attached edges, and assume Kirchhoff-Neumann conditions hold at the internal vertices. Associated to this graph is a Schrödin…