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  1. Applied Mathematics-A Journal of Chinese Universities
  2. Applied Mathematics-A Journal of Chinese Universities : Volume 22
  3. Applied Mathematics-A Journal of Chinese Universities : Volume 22, Issue 3, September 2007
  4. Exact boundary controllability of 1-D nonlinear Schrödinger equation
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Applied Mathematics-A Journal of Chinese Universities : Volume 32
Applied Mathematics-A Journal of Chinese Universities : Volume 31
Applied Mathematics-A Journal of Chinese Universities : Volume 30
Applied Mathematics-A Journal of Chinese Universities : Volume 29
Applied Mathematics-A Journal of Chinese Universities : Volume 28
Applied Mathematics-A Journal of Chinese Universities : Volume 27
Applied Mathematics-A Journal of Chinese Universities : Volume 26
Applied Mathematics-A Journal of Chinese Universities : Volume 25
Applied Mathematics-A Journal of Chinese Universities : Volume 24
Applied Mathematics-A Journal of Chinese Universities : Volume 23
Applied Mathematics-A Journal of Chinese Universities : Volume 22
Applied Mathematics-A Journal of Chinese Universities : Volume 22, Issue 4, December 2007
Applied Mathematics-A Journal of Chinese Universities : Volume 22, Issue 3, September 2007
Asymptotic theory for a risk process with a high dividend barrier
Analysis of two-dimensional electromagnetic scattering by a perfectly conducting obstacle in a homogeneous chiral environment
Scale and time effects on mathematical models for transport in the environment
Exact boundary controllability of 1-D nonlinear Schrödinger equation
Nonlinear reaction diffusion problems with ultra parabolic limiting equations
Existence of solution for boundary value problem of nonlinear fractional differential equation
Convergence rate of vector subdivision scheme
Strong convergence of approximated sequences for nonexpansive mappings in Banach spaces
Maximal inequality and complete convergences of non-identically distributed negatively associated sequences
Some comparisons between generalized order statistics
Exponential estimates for stochastic delay hybrid systems with Markovian switching
Stochastic flows of mappings
Homocentric convergence ball of the secant method
Some extended knapsack problems involving job partition between two parties
Geometric properties for Gaussian image of submanifolds in S $^{ n+p }$(1)
Applied Mathematics-A Journal of Chinese Universities : Volume 22, Issue 2, June 2007
Applied Mathematics-A Journal of Chinese Universities : Volume 22, Issue 1, March 2007
Applied Mathematics-A Journal of Chinese Universities : Volume 21
Applied Mathematics-A Journal of Chinese Universities : Volume 20
Applied Mathematics-A Journal of Chinese Universities : Volume 19
Applied Mathematics-A Journal of Chinese Universities : Volume 18
Applied Mathematics-A Journal of Chinese Universities : Volume 17
Applied Mathematics-A Journal of Chinese Universities : Volume 16
Applied Mathematics-A Journal of Chinese Universities : Volume 15
Applied Mathematics-A Journal of Chinese Universities : Volume 14
Applied Mathematics-A Journal of Chinese Universities : Volume 13
Applied Mathematics-A Journal of Chinese Universities : Volume 12

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Exact boundary controllability of 1-D nonlinear Schrödinger equation

Content Provider Springer Nature Link
Author Zong, Xiju Zhao, Yi Yin, Zhaoyang Chi, Tao
Copyright Year 2007
Abstract In this paper, the boundary control problem of a distributed parameter system described by the Schrödinger equation posed on finite interval α ≤ x ≤ β: $$\left\{ \begin{gathered} iy_t + y_{xx} + |y|^2 y = 0, \enspace\enspace \\ y(\alpha ,t) = h_1 (t),y(\beta ,t) = h_2 (t)fort > 0 \enspace\enspace \\ \end{gathered} \right.(S)$$ is considered. It is shown that by choosing appropriate control inputs (h $_{j}$), (j = 1, 2) one can always guide the system (S) from a given initial state φ ∈ H $^{s}$(α, β), (s ∈ R) to a terminal state ψ ∈ H $^{s}$(α, β), in the time period [0, T]. The exact boundary controllability is obtained by considering a related initial value control problem of Schrödinger equation posed on the whole line R. The discovered smoothing properties of Schrödinger equation have played important roles in our approach; this may be the first step to prove the results on boundary controllability of (semi-linear) nonlinear Schrödinger equation.
Starting Page 277
Ending Page 285
Page Count 9
File Format PDF
ISSN 10051031
Journal Applied Mathematics-A Journal of Chinese Universities
Volume Number 22
Issue Number 3
e-ISSN 19930445
Language English
Publisher Editorial Committee of Applied Mathematics
Publisher Date 2007-01-01
Publisher Place Hangzhou
Access Restriction One Nation One Subscription (ONOS)
Subject Keyword nonlinear Schrödinger equation exact boundary controllability Hilbert uniqueness method Mathematics Applications of Mathematics
Content Type Text
Resource Type Article
Subject Applied Mathematics
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