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Regularity of solutions and controllability of evolution equations associated with non-selfadjointoperators

Abstract : The subject of this thesis deals with the sharp microlocal study of the smoothing and decreasing properties of evolution equations associated with two classes of non-selfadjoint operators with applications to the study of their subelliptic properties and to the null-controllability of these equations. The first class is composed of non-local operators given by the Ornstein-Uhlenbeck operators defined as the sum of a fractional diffusion and a linear transport operator. The second class is the class of accretive quadratic differential operators given by the Weyl quantization of complex-valued quadratic forms defined on the phase space with non-negative real parts. The aim of this work is to understand how the possible non-commutation phenomena between the self-adjoint and the skew-selfadjoint parts of these operators allow the associated semigroups to enjoy smoothing and decreasing properties in specific directions of the phase space that are explicitly described.
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Submitted on : Thursday, July 9, 2020 - 10:49:09 AM
Last modification on : Saturday, July 11, 2020 - 3:14:16 AM


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Paul Alphonse. Regularity of solutions and controllability of evolution equations associated with non-selfadjointoperators. Analysis of PDEs [math.AP]. Université Rennes 1, 2020. English. ⟨NNT : 2020REN1S003⟩. ⟨tel-02894736⟩



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