A Null-Controllability Result for the Linear System of Thermoelastic Plates with a Single Control

2017 ◽  
pp. 77-89
Author(s):  
Carlos Castro ◽  
Luz De Teresa
Keyword(s):  
Linear System ◽  
Null Controllability ◽  
Thermoelastic Plates ◽  
Controllability Result

Null controllability of fractional dynamical systems with constrained control

2017 ◽  
Vol 20 (2) ◽  
Author(s):  
Rajagopal Joice Nirmala ◽  
Krishnan Balachandran ◽  
Juan J. Trujillo
Keyword(s):  
Dynamical Systems ◽  
Nonlinear System ◽  
Linear System ◽  
Sufficient Conditions ◽  
Null Controllability ◽  
Constrained Control

AbstractThis paper concerns the null controllability of fractional dynamical systems with constrained control. We assume that the linear system is controllable with square integrable control and provide sufficient conditions for the null controllability with constrained control. Further, sufficient conditions for the null controllability of nonlinear system also are established. Examples are provided to illustrate the theory.

scholarly journals Uniform null controllability for a parabolic equations with discontinuous diffusion coefficient

2021 ◽  
Author(s):  
Jérémi Dardé ◽  
Sylvain Ervedoza ◽  
Roberto Morales
Keyword(s):  
Diffusion Coefficient ◽  
Heat Equation ◽  
Parabolic Equations ◽  
Null Controllability ◽  
Wave Operators ◽  
Conductive Medium ◽  
Geometric Conditions ◽  
Discontinuous Diffusion ◽  
Controllability Result

In this article, we study the null-controllability of a heat equation in a domain composed of two media of different constant conductivities. In particular, we are interested in the behavior of the system when the conductivity of the medium on which the control does not act goes to infinity, corresponding at the limit to a perfectly conductive medium. In that case, and under suitable geometric conditions, we obtain a uniform null-controllability result. Our strategy is based on   the analysis of the controllability of the corresponding wave operators and the transmutation technique, which explains the geometric conditions.

scholarly journals Exact Null Controllability for Fractional Nonlocal Integrodifferential Equations via Implicit Evolution System

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Amar Debbouche ◽  
Dumitru Baleanu
Keyword(s):  
Banach Space ◽  
Strong Solutions ◽  
Existence Results ◽  
Null Controllability ◽  
Evolution System ◽  
Integrodifferential System ◽  
Exact Null Controllability ◽  
Nonlinear Integrodifferential System ◽  
Nonlocal Nonlinear ◽  
Controllability Result

We introduce a new concept called implicit evolution system to establish the existence results of mild and strong solutions of a class of fractional nonlocal nonlinear integrodifferential system, then we prove the exact null controllability result of a class of fractional evolution nonlocal integrodifferential control system in Banach space. As an application that illustrates the abstract results, two examples are provided.

scholarly journals Null-controllability of perturbed porous medium gas flow

2020 ◽  
Vol 26 ◽  
pp. 85
Author(s):  
Borjan Geshkovski
Keyword(s):  
Porous Medium ◽  
Gas Flow ◽  
Porous Medium Equation ◽  
Null Controllability ◽  
Spectral Techniques ◽  
Medium Equation ◽  
Self Similar Solution ◽  
Linearized Problem ◽  
Thin Film Equation ◽  
Controllability Result

In this work, we investigate the null-controllability of a nonlinear degenerate parabolic equation, which is the equation satisfied by a perturbation around the self-similar solution of the porous medium equation in Lagrangian-like coordinates. We prove a local null-controllability result for a regularized version of the nonlinear problem, in which singular terms have been removed from the nonlinearity. We use spectral techniques and the source-term method to deal with the linearized problem and the conclusion follows by virtue of a Banach fixed-point argument. The spectral techniques are also used to prove a null-controllability result for the linearized thin-film equation, a degenerate fourth order analog of the problem under consideration.

scholarly journals Controllability of degenerate and singular parabolic problems: the double strong case with Neumann boundary conditions

2019 ◽  
Vol 39 (2) ◽  
pp. 207-225 ◽  
Author(s):  
Genni Fragnelli ◽  
Dimitri Mugnai
Keyword(s):  
Boundary Conditions ◽  
Parabolic Problem ◽  
Singular Potential ◽  
Neumann Boundary ◽  
Null Controllability ◽  
Neumann Boundary Conditions ◽  
Parabolic Problems ◽  
Smooth Coefficients ◽  
Strongly Degenerate ◽  
Controllability Result

We prove a null controllability result for a parabolic problem with Neumann boundary conditions. We consider non smooth coefficients in presence of a strongly singular potential and a strongly degenerate coefficient, both vanishing at an interior point. This paper concludes the study of the Neumann case.

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