Zobrazeno 1 - 10
of 127
pro vyhledávání: '"Avdonin, Sergei"'
Let $\Delta$ be the Dirichlet Laplacian on the interval $(0,\pi)$. The null controllability properties of the equation $$u_{tt}+\Delta^2 u+\rho (\Delta)^\alpha u_t=F(x,t)$$ are studied. Let $T>0$, and assume initial conditions $(u^0,u^1)\in Dom(\Delt
Externí odkaz:
http://arxiv.org/abs/2401.14987
Publikováno v:
Bolet\'in de la Sociedad Matem\'atica Mexicana v. 29 (2023), Art. 82. (Open Access)
A method for successive synthesis of a Weyl matrix (or Dirichlet-to-Neumann map) of an arbitrary quantum tree is proposed. It allows one, starting from one boundary edge, to compute the Weyl matrix of a whole quantum graph by adding on new edges and
Externí odkaz:
http://arxiv.org/abs/2308.01911
Publikováno v:
Math Meth Appl Sci 2024
The inverse problem of recovery of a potential on a quantum tree graph from Weyl's matrix given at a number of points is considered. A method for its numerical solution is proposed. The overall approach is based on the leaf peeling method combined wi
Externí odkaz:
http://arxiv.org/abs/2302.05970
Autor:
Avdonin, Sergei A., Edward, Julian K.
In this paper we study the exact controllability problem for the wave equation on a finite metric graph with the Kirchhoff-Neumann matching conditions. Among all vertices and edges we choose certain active vertices and edges, and give a constructive
Externí odkaz:
http://arxiv.org/abs/2301.10269
In this paper, we consider the inverse dynamic problem for the Dirac system on finite metric tree graphs. Our main goal is to recover the topology (connectivity) of a tree, lengths of edges, and a matrix potential function on each edge. We use the dy
Externí odkaz:
http://arxiv.org/abs/2210.16869
Publikováno v:
Inverse Problems and Imaging, 2024,18(1) 311-325
The problem of recovery of a potential on a quantum star graph from Weyl's matrix given at a finite number of points is considered. A method for its approximate solution is proposed. It consists in reducing the problem to a two-spectra inverse Sturm-
Externí odkaz:
http://arxiv.org/abs/2210.15536
Publikováno v:
Journal of Inverse and Ill-Posed Problems 2023 (31) 31-42
A new method for solving inverse spectral problems on quantum star graphs is proposed. The method is based on Neumann series of Bessel functions representations for solutions of Sturm-Liouville equations. The representations admit estimates for the s
Externí odkaz:
http://arxiv.org/abs/2210.12500
The question of what conditions should be set at the nodes of a discrete graph for the wave equation with discrete time is investigated. The variational method for the derivation of these conditions is used. A parallel with the continuous case is als
Externí odkaz:
http://arxiv.org/abs/2210.09274
Exact controllability for the wave equation on a metric graph consisting of a cycle and two attached edges is proven. One boundary and one internal control are used. At the internal vertices, delta-prime conditions are satisfied. As a second example,
Externí odkaz:
http://arxiv.org/abs/2210.03790
Exact controllability is proven on a graph with cycle. The controls can be a mix of controls applied at the boundary and interior vertices. The method of proof first uses a dynamical argument to prove shape controllability and velocity controllabilit
Externí odkaz:
http://arxiv.org/abs/2210.03344