Julian Edward

collaborators

4 papers

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 $I^$ be the Neumann Laplacian on the interval $(0, I ¨ )$ , and let $T > 0$ . An integration by parts formula is proven for the spectral fractional Laplacian, $(- I^)^{I^} \pm$ , for $Î±\in (…

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 $I^$ be the Dirichlet Laplacian on a bounded domain $I^c ◯ \subset R^{N}$ , and let $(- I^)^{I^} \pm$ be the associated spectral fractional Laplacian with $I^\pm \leq 1, I ¨ < 2$ . For…

math.OC2026

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

Sergei Avdonin, Julian Edward

Let $I^$ be the Dirichlet Laplacian on the interval $(0, I ¨ )$ , and let $T > 0$ . We prove a well-posedness results for the structurally damped beam equation $$u_{tt}+Î^2 u-ÏÎu_t=0,…

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 SchrÃ¶di…