scholarly journals Geometric conditions for the null-controllability of hypoelliptic quadratic parabolic equations with moving control supports

2020 ◽  
Vol 358 (6) ◽  
pp. 651-700
Author(s):  
Karine Beauchard ◽  
Michela Egidi ◽  
Karel Pravda-Starov
Keyword(s):  
Parabolic Equations ◽  
Null Controllability ◽  
Geometric Conditions

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 Carleman estimates and null controllability of a class of singular parabolic equations

2018 ◽  
Vol 8 (1) ◽  
pp. 1057-1082
Author(s):  
Runmei Du ◽  
Jürgen Eichhorn ◽  
Qiang Liu ◽  
Chunpeng Wang
Keyword(s):  
Control Systems ◽  
Parabolic Equations ◽  
Null Controllability ◽  
Carleman Estimates ◽  
Energy Estimates ◽  
Semilinear Parabolic Equations ◽  
Linearized Equations ◽  
Singular Parabolic Equations ◽  
Semilinear Parabolic

Abstract In this paper, we consider control systems governed by a class of semilinear parabolic equations, which are singular at the boundary and possess singular convection and reaction terms. The systems are shown to be null controllable by establishing Carleman estimates, observability inequalities and energy estimates for solutions to linearized equations.

scholarly journals QUADRATIC DIFFERENTIAL EQUATIONS: PARTIAL GELFAND–SHILOV SMOOTHING EFFECT AND NULL-CONTROLLABILITY

2020 ◽  
pp. 1-53
Author(s):  
Paul Alphonse
Keyword(s):  
Euclidean Space ◽  
Quadratic Differential ◽  
Parabolic Equations ◽  
Evolution Equations ◽  
Differential Operators ◽  
Null Controllability ◽  
Geometric Condition ◽  
Positive Time ◽  
Regularizing Effects ◽  
Necessary And Sufficient

We study the partial Gelfand–Shilov regularizing effect and the exponential decay for the solutions to evolution equations associated with a class of accretive non-selfadjoint quadratic operators, which fail to be globally hypoelliptic on the whole phase space. By taking advantage of the associated Gevrey regularizing effects, we study the null-controllability of parabolic equations posed on the whole Euclidean space associated with this class of possibly non-globally hypoelliptic quadratic operators. We prove that these parabolic equations are null-controllable in any positive time from thick control subsets. This thickness property is known to be a necessary and sufficient condition for the null-controllability of the heat equation posed on the whole Euclidean space. Our result shows that this geometric condition turns out to be a sufficient one for the null-controllability of a large class of quadratic differential operators.

scholarly journals Null Controllability of One-dimensional Parabolic Equations by the Flatness Approach

2016 ◽  
Vol 54 (1) ◽  
pp. 198-220 ◽  
Author(s):  
Philippe Martin ◽  
Lionel Rosier ◽  
Pierre Rouchon
Keyword(s):  
Parabolic Equations ◽  
Null Controllability ◽  
One Dimensional
Sign in / Sign up

Export Citation Format

Share Document