Controllability for Schrödinger type system with mixed dispersion on compact star graphs
نویسندگان
چکیده
In this work we are concerned with solutions to the linear Schr\"odinger type system mixed dispersion, so-called biharmonic equation. Precisely, able prove an exact control property for these in energy space posed on oriented star graph structure $\mathcal{G}$ $T>T_{min}$, $$T_{min}=\sqrt{ \frac{ \overline{L} (L^2+\pi^2)}{\pi^2\varepsilon(1- \varepsilon)}},$$ when couplings and controls appear only Neumann boundary conditions.
منابع مشابه
Global Controllability and Stabilization for the Nonlinear Schrödinger Equation on Some Compact Manifolds of Dimension 3
We prove global internal controllability in large time for the nonlinear Schrödinger equation on some compact manifolds of dimension 3. The result is proved under some geometrical assumptions : geometric control and unique continuation. We give some examples where they are fulfilled on T3, S3 and S2 × S1. We prove this by two different methods both inherently interesting. The first one combines...
متن کاملAmbarzumyan–type Theorems on Star Graphs
The so-called Ambarzumyan theorem states that if the Neumann eigenvalues of the Sturm-Liouville operator − d2 dx2 +q with an integrable real-valued potential q on [0,π] are {n2 : n 0} , then q = 0 for almost all x ∈ [0,π] . In this work, the classical Ambarzumyan theorem is extended to star graphs with Dirac operators on its edges. We prove that if the spectrum of Dirac operator on star graphs ...
متن کاملSchrödinger equations in noncylindrical domains: exact controllability
We consider an open bounded set Ω ⊂ Rn and a family {K(t)}t≥0 of orthogonal matrices of Rn. Set Ωt = {x ∈Rn; x = K(t)y, for all y ∈Ω}, whose boundary is Γt. We denote by ̂ Q the noncylindrical domain given by ̂ Q =⋃0<t<T{Ωt ×{t}}, with the regular lateral boundary ̂ ∑ = ⋃0<t<T{Γt × {t}}. In this paper we investigate the boundary exact controllability for the linear Schrödinger equation u′ − iΔu= f...
متن کاملOn Edge-Decomposition of Cubic Graphs into Copies of the Double-Star with Four Edges
A tree containing exactly two non-pendant vertices is called a double-star. Let $k_1$ and $k_2$ be two positive integers. The double-star with degree sequence $(k_1+1, k_2+1, 1, ldots, 1)$ is denoted by $S_{k_1, k_2}$. It is known that a cubic graph has an $S_{1,1}$-decomposition if and only if it contains a perfect matching. In this paper, we study the $S_{1,2}$-decomposit...
متن کاملApproximate controllability of the Schrödinger equation with a polarizability term
This paper is concerned with the controllability of quantum systems in the case where the standard dipolar approximation, involving the permanent dipole moment of the system, has to be corrected by a so-called polarizability term, involving the field induced dipole moment. Sufficient conditions for controllability between eigenstates of the free Hamiltonian are derived and control laws are expl...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Evolution Equations and Control Theory
سال: 2023
ISSN: ['2163-2472', '2163-2480']
DOI: https://doi.org/10.3934/eect.2022019