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Power Geometry
Springer Science and Business Media LLC - Tập 3 - Trang 471-491 - 1997
A. D. Bruno
All local and asymptotic first approximations of a polynomial, a differential polynomial, and of a system of such polynomials can be selected algorithmically. Here the first approximation of a solution to the system of equations is a solution to the corresponding first approximation of the system of equations. The power transformations induce linear transformations of vector exponents and commute ...... hiện toàn bộ
Stabilization of One-Dimensional Schrödinger Equation Under Joint Feedback Control with Delayed Observation
Springer Science and Business Media LLC - Tập 25 - Trang 275-288 - 2018
K. Y. Yang
In this paper, we consider a one-dimensional Schrödinger equation under a joint linear feedback control at an arbitrary internal point $\xi (0<\xi <1)$ . It is shown that the pointwise control system is asymptotically stable if ...... hiện toàn bộ
Efficient controls for traffic flow on networks
Springer Science and Business Media LLC - Tập 16 - Trang 407-437 - 2010
C. D’Apice, P. I. Kogut, R. Manzo
We study traffic flow models for road networks in vector-valued optimization statement, where the flow is controlled at the nodes of the network. We consider the case where an objective mapping possesses a weakened property of upper semicontinuity and make no assumptions on the interior of the ordering cone. We derive sufficient conditions for the existence of efficient controls of the traffic pro...... hiện toàn bộ
Existence and Controllability for Impulsive Evolution Inclusions without Compactness
Springer Science and Business Media LLC - Tập 24 - Trang 297-311 - 2017
Yong Zhou, S. Suganya, M. Mallika Arjunan
In this paper, we investigate the existence and controllability for impulsive evolution inclusions in Banach spaces. By using weak topology technique and Glicksberg-Ky Fan fixed point theorem, we obtain the existence of mild solutions and controllability outcomes, avoiding hypotheses of compactness on the semigroup generated by the linear part and any conditions on the multivalued nonlinearity exp...... hiện toàn bộ
A Geometric Criterion for the Existence of Chaos Based on Periodic Orbits in Continuous-Time Autonomous Systems
Springer Science and Business Media LLC - Tập 29 Số 1 - Trang 71-93 - 2023
Xu Zhang, Guanrong Chen
Exponential Stabilization for the Nonlinear Schrödinger Equation with Localized Damping
Springer Science and Business Media LLC - Tập 21 - Trang 461-474 - 2015
Fábio Natali
Results of exponential stability related to the nonlinear Schrödinger equation posed on the whole real line will be discussed in this paper. We shall use local smoothing effect associated with the semigroup of the Schrödinger equation, Strichartz estimates, and compactness tools to determine the exponential decay of the energy, by assuming the initial data in convenient bounded sets of L ...... hiện toàn bộ
Analysis of Inhomogeneous Boundary Value Problems for Generalized Boussinesq Model of Mass Transfer
Springer Science and Business Media LLC - Tập 29 - Trang 1809-1828 - 2023
Brizitskii R.V., Saritskaia Zh. Yu.
The global solvability of the boundary value problem for the nonlinear mass transfer equations is proved under inhomogeneous Dirichlet boundary conditions for the velocity given on the entire boundary, and for the substance’s concentration, given on the part of the boundary. It is assumed that the reaction coefficient in one of the equations of the model depends nonlinearly on the substance’s conc...... hiện toàn bộ
Coalescence of Two Regular Singularities into One Regular Singularity for the Linear Ordinary Differential Equation
Springer Science and Business Media LLC - Tập 7 - Trang 127-149 - 2001
A. Ya. Kazakov
The process of coalescence of two regular singular points of linear ODE into a single regular singularity is studied. This problem is examined in terms of connection matrices and solutions of the corresponding equations.
On the coincidence of two manifolds associated with the Calogero model
Springer Science and Business Media LLC - Tập 15 - Trang 393-403 - 2009
V. Meshcheryakov
Let R be a root system, for example, the root system associated to a semisimple Lie algebra. In [1], V. A. Golubeva and V. P. Lexin constructed two algebraic manifolds (Bethe and Dunkl manifolds) using the “universal” Dunkl operators. These manifolds were defined as subsets of the complex space ℂ N of dimension equal to the number of roots of the root system unde...... hiện toàn bộ
Stabilization of General Nonlinear Control Systems via Center Manifold and Approximation Techniques
Springer Science and Business Media LLC - Tập 10 - Trang 315-327 - 2004
Daizhan Cheng, Zairong Xi, Gang Feng
This paper considers the stabilization of a class of general nonlinear control systems. Under some mild conditions, a general nonlinear control system can be transformed into a normal form, which is suitable for the center manifold approach. A kind of controller in the polynomial form is proposed to stabilize the systems. First, the type and degree of controllers are chosen to assure the approxima...... hiện toàn bộ
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