14 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 $α\in (…
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…
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}+Î^2 u-ÏÎu_t=0,…
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…
On some applications of the Boundary Control method to spectral estimation and inverse problems
S. A. Avdonin, A. S. Mikhaylov, V. S. Mikhaylov
We consider applications of the Boundary Control (BC) method to generalized spectral estimation problems and to inverse source problems. We derive the equations of the BC method fo…
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 Schrödi…