Quadratic differential equations : partial Gelfand-Shilov smoothing effect and null-controllability

Paul Alphonse

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arXiv · 1902.04459

Quadratic differential equations : partial Gelfand-Shilov smoothing effect and null-controllability

Paul Alphonse

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Abstract

We study the partial Gelfand-Shilov regularizing effect and the exponential decay for the solutions to evolution equations associated to 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 to 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.

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Paul Alphonse. 2019-02-12. Quadratic differential equations : partial Gelfand-Shilov smoothing effect and null-controllability. https://arxiv.org/abs/1902.04459

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