scholarly journals Null-controllability of hypoelliptic quadratic differential equations

2018 ◽  
Vol 5 ◽  
pp. 1-43 ◽  
Author(s):  
Karine Beauchard ◽  
Karel Pravda-Starov
Keyword(s):  
Differential Equations ◽  
Quadratic Differential ◽  
Null Controllability

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 fractional stochastic delay integro-differential equations

2019 ◽  
Vol 19 (03) ◽  
pp. 143-150 ◽  
Author(s):  
Hamdy M. Ahmed ◽  
Mahmoud M. El-Borai ◽  
H. M. El-Owaidy ◽  
A. S. Ghanem
Keyword(s):  
Differential Equations ◽  
Null Controllability ◽  
Stochastic Delay

scholarly journals Research of Chaotic Dynamics of 3D Autonomous Quadratic Systems by Their Reduction to Special 2D Quadratic Systems

2015 ◽  
Vol 2015 ◽  
pp. 1-15 ◽  
Author(s):  
Vasiliy Belozyorov
Keyword(s):  
Differential Equations ◽  
Quadratic Differential ◽  
Chaotic Dynamics ◽  
Quadratic System ◽  
System Of Differential Equations ◽  
Quadratic Systems

New results about the existence of chaotic dynamics in the quadratic 3D systems are derived. These results are based on the method allowing studying dynamics of 3D system of autonomous quadratic differential equations with the help of reduction of this system to the special 2D quadratic system of differential equations.

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