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Pointwise Controllability for Degenerate Parabolic Equations by the Moment Method
Springer Science and Business Media LLC - Tập 26 - Trang 349-362 - 2020
Brahim Allal, Jawad Salhi
In this paper, we study the pointwise controllability of the one-dimensional degenerate heat equation. Necessary and sufficient conditions for approximate and null controllability are proved. Our approach is mainly based on the moment method developed by Fattorini and Russell.
Stabilization of the Viscoelastic Wave Equation with Variable Coefficients and a Delay Term in Nonlocal Boundary Feedback
Springer Science and Business Media LLC - Tập 30 Số 1 - Trang 1-24 - 2024
Li, Sheng-Jie, Chai, Shugen
In this paper, we investigate the viscoelastic wave equation with variable coefficients and a delay, which is subject to nonlinear and nonlocal boundary dissipation. The existence of strong and weak solutions is obtained by means of Faedo-Galerkin approximation and denseness argument. By introducing an equivalent energy functional and using the Riemannian geometry method, we show the general decay...... hiện toàn bộ
Time-optimal control problem for co-operative hyperbolic systems involving the Laplace operator
Springer Science and Business Media LLC - Tập 15 - Trang 405-423 - 2009
H. A. El-Saify, H. M. Serag, M. A. Shehata
In this paper, the time-optimal control problem for (2 × 2)-co-operative hyperbolic system with variable coefficients and involving Laplace operator is considered. This problem is, steering the initial state ((y(0), y′(0)) so that the observation z(t) hitting a given target set in minimum time. For different cases of the observation, the time-optimal controls are characterized in terms of the adjo...... hiện toàn bộ
Functional Series Expansions for Continuous-Time Switched Systems
Springer Science and Business Media LLC - Tập 21 - Trang 211-237 - 2014
Luis A. Duffaut Espinosa, W. Steven Gray
The main objective of this paper is to describe a class of functional series expansions, known as Fliess operators, which admit inputs from a ball in an L p space as well as Poisson random processes. Conditions are given under which these functional series expansions converge absolutely in the mean. Then, it is shown that a continuous-time switch...... hiện toàn bộ
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
A Remark on the Invertibility of Semi-invertible Cocycles
Springer Science and Business Media LLC - Tập 25 - Trang 527-533 - 2018
Lucas Backes
We observe that under certain conditions on the Lyapunov exponents, a semi-invertible cocycle is, indeed, invertible. As a consequence, if a semi-invertible cocycle generated by a Hölder continuous map $A:\mathcal {M}\to M(d, \mathbb {R})$ over a...... hiện toàn bộ
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