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

scholarly journals Null controllability for a class of stochastic singular parabolic equations with the convection term

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Lin Yan ◽  
Bin Wu
Keyword(s):  
Parabolic Equations ◽  
Dimensional Space ◽  
Adjoint System ◽  
Null Controllability ◽  
Observability Inequality ◽  
Convection Term ◽  
One Dimensional ◽  
Singular Parabolic Equation ◽  
Approximate System ◽  
Singular Parabolic Equations

<p style='text-indent:20px;'>This paper concerns the null controllability for a class of stochastic singular parabolic equations with the convection term in one dimensional space. Due to the singularity, we first transfer to study an approximate nonsingular system. Next we establish a new Carleman estimate for the backward stochastic singular parabolic equation with convection term and then an observability inequality for the adjoint system of the approximate system. Based on this observability inequality and an approximate argument, we obtain the null controllability result.</p>

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