47 citations · 248 across the 29 of their papers we have counts for
30 papers
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 be the Neumann Laplacian on the interval , and let . An integration by parts formula is proven for the spectral fractional Laplacian, , for …
A symmetry formula for the spectral fractional Laplacian, and applications to boundary controllability for plate equation with structural damping
Sergei Avdonin, Julian Edward
Let be the Dirichlet Laplacian on a bounded domain , and let be the associated spectral fractional Laplacian with . For genera…
Boundary null-controllability for the beam equation with classical structural damping
Sergei Avdonin, Julian Edward
Let be the Dirichlet Laplacian on the interval , and let . We prove a well-posedness results for the structurally damped beam equation $$u_{tt}+Δ^2 u-ρΔu_t=0, x\in…
An inverse problem for semilinear wave equations on metric tree graphs
Sergei Avdonin, Matti Lassas, Jinpeng Lu +2
We study the inverse problem for a semilinear wave equation on metric tree graphs. From the Dirichlet-to-Neumann map defined at all but one of the boundary vertices, we recover unk…
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…
The boundary control approach to the Titchmarsh-Weyl function
S. A. Avdonin, V. S. Mikhaylov, A. V. Rybkin
We link the Boundary Control Theory and the Titchmarsh-Weyl Theory. This provides a natural interpretation of the amplitude due to Simon and yields a new efficient method to ev…