scholarly journals A uniform controllability result for the Keller–Segel system

2015 ◽  
Vol 92 (3-4) ◽  
pp. 313-338 ◽  
Author(s):  
Felipe Wallison Chaves-Silva ◽  
Sergio Guerrero
Keyword(s):  
Uniform Controllability ◽  
Controllability Result

scholarly journals On the uniform controllability for a family of non-viscous and viscous Burgers-α systems

2021 ◽  
Author(s):  
Diego Araujo de Souza ◽  
Raul K. C. Araujo ◽  
Enrique Fernández-Cara
Keyword(s):  
Burgers Equation ◽  
Wave Length ◽  
Exact Controllability ◽  
Convective Velocity ◽  
Distributed Controls ◽  
Target States ◽  
Controllability Property ◽  
Return Method ◽  
Uniform Controllability ◽  
Controllability Result

In this paper we study the global controllability of families of the so called non-viscous and viscous Burgers-α systems by using boundary and space independent distributed controls. In these equations, the usual convective velocity of the Burgers equation is replaced by a regularized velocity, induced by a Helmholtz filtered of characteristic wave-length α. First, we prove a global exact controllability result (uniform with respect to α) for the non-viscous Burgers-α system, using the return method and a fixed-point argument. Then, the global uniform exact controllability to constant states is deduced for the viscous equations. To this purpose, we first prove a local exact controllability property and, then, we establish a global approximate controllability result for smooth initial and target states.

scholarly journals Controllability result for nonlinear evolution integrodifferential systems

2004 ◽  
Vol 17 (9) ◽  
pp. 1015-1023 ◽  
Author(s):  
R. Sakthivel ◽  
Q.H. Choi ◽  
S.M. Anthony
Keyword(s):  
Nonlinear Evolution ◽  
Controllability Result

scholarly journals Uniform controllability properties for space/time-discretized parabolic equations

2011 ◽  
Vol 118 (4) ◽  
pp. 601-661 ◽  
Author(s):  
Franck Boyer ◽  
Florence Hubert ◽  
Jérôme Le Rousseau
Keyword(s):  
Parabolic Equations ◽  
Space Time ◽  
Uniform Controllability

scholarly journals Controllability of Impulsive Fractional Functional Integro-Differential Equations in Banach Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
C. Ravichandran ◽  
J. J. Trujillo
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Fractional Calculus ◽  
Banach Spaces ◽  
Mixed Type ◽  
Sufficient Conditions ◽  
Controllability Problem ◽  
Controllability Result ◽  
Fractional Functional

This paper is concerned with the controllability problem for a class of mixed type impulsive fractional integro-differential equations in Banach spaces. Sufficient conditions for the controllability result are established by using suitable fixed point theorem combined with the fractional calculus theory and solution operator under some weak conditions. The example is given in illustrate the theory. The results of this article are generalization and improved of the recent results on this issue.

scholarly journals Controllability of Fractional Neutral Stochastic Integro-Differential Systems with Infinite Delay

2013 ◽  
Vol 2013 ◽  
pp. 1-10
Author(s):  
Xichao Sun ◽  
Litan Yan ◽  
Jing Cui
Keyword(s):  
Fixed Point ◽  
Fractional Calculus ◽  
Infinite Delay ◽  
Sufficient Conditions ◽  
Abstract Space ◽  
Differential Systems ◽  
Compactness Condition ◽  
Fixed Point Principle ◽  
Controllability Result

This paper is concerned with the controllability of a class of fractional neutral stochastic integro-differential systems with infinite delay in an abstract space. By employing fractional calculus and Sadovskii's fixed point principle without assuming severe compactness condition on the semigroup, a set of sufficient conditions are derived for achieving the controllability result.

scholarly journals Existence and controllability result for semilinear evolution integrodifferential systems

2005 ◽  
Vol 41 (8-9) ◽  
pp. 1005-1011 ◽  
Author(s):  
R. Sakthivel ◽  
S.M. Anthoni ◽  
J.H. Kim
Keyword(s):  
Controllability Result

Approximate Controllability of Boundary Control Systems with Nonlinear Boundary Conditions

2014 ◽  
Vol 538 ◽  
pp. 408-412
Author(s):  
Lian Wen Wang
Keyword(s):  
Boundary Conditions ◽  
Control Systems ◽  
Linear Systems ◽  
Boundary Control ◽  
Approximate Controllability ◽  
Nonlinear Boundary ◽  
Nonlinear Boundary Conditions ◽  
Boundary Control Systems ◽  
Delayed Control Systems ◽  
Controllability Result

The paper deals with the approximate controllability of a class of nonlinear delayed control systems in which the control is acted through the boundary of the region and the boundary conditions are nonlinear. The approximate controllability result is established provided the approximate controllability of the corresponding linear systems.

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