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# Séminaire Analyse

Les exposés couvrent essentiellement les thématiques autour de l’analyse complexe, la théorie des opérateurs, l’analyse harmonique, l’analyse fonctionnelle, la théorie spectrale et la modélisation et le signal (responsables : Mohamed Zarrabi et Stanislas Kupin)

• Le 27 juin 2022 à 14:00
• Salle 2
Shirshendu Chowdhury (IISER Kolkata)
!!! ATTENTION CRENEAU INHABITUEL !!! Boundary null-controllability of 1d linearized compressible Navier-Stokes System by one control force.
In the first part of the talk, we introduce the concept: Controllability of Differential Equations. Then we give some examples in finite (ODE) and infinitedimensional(PDE) contexts. We recall the controllability results of the Transport and Heat equation.In the second part of the talk, we consider compressible Navier-Stokes equations in one dimension, linearized around a constant steady state (Q_0, V_0 ) , with Q_ 0 > 0, V 0 >0 . It is a Coupled system of transport and heat type equations. We study the boundary null-controllability of thislinearized system in the interval $(0,1)$ when a Dirichlet control function is acting either only on the density or only on the velocity component at oneend of the interval. We obtain null controllability using one boundary control in the space ${H}^s_{per}(0,1)times L^2(0,1)$ for any $s>frac{1}{2}$provided the time $T>1$, where ${H}_{per}^s(0,1)$ denotes the Sobolev space of periodic functions. The proof is based on a spectral analysis and onsolving a mixed parabolic-hyperbolic moments problem and a parabolic-hyperbolic joint Ingham-type inequality. This is a recent joint work (https://arxiv.org/abs/2204.02375, 2022) with Kuntal Bhandari, Rajib Dutta and Jiten Kumbhakar.

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