On an estimate connected with the stabilization of normal parabolic equation by start control
Fundamentalʹnaâ i prikladnaâ matematika, Tome 19 (2014) no. 4, pp. 197-230.

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After a brief revision of facts concerning semilinear parabolic equations of normal type and their nonlocal stabilization by start control, we provide a simplification of the proof of the lower bound for a functional of the solution to the heat equation with initial condition of a special type. This bound is essential to prove the nonlocal stabilization of equations of normal type. The simplification presented is required for further development of the nonlocal stabilization theory.
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A. V. Fursikov; L. S. Shatina. On an estimate connected with the stabilization of normal parabolic equation by start control. Fundamentalʹnaâ i prikladnaâ matematika, Tome 19 (2014) no. 4, pp. 197-230. http://geodesic.mathdoc.fr/item/FPM_2014_19_4_a6/

[1] Fursikov A. V., Emanuilov Yu. S., “Tochnaya upravlyaemost uravnenii Nave–Stoksa i Bussineska”, Uspekhi mat. nauk, 54:3(227) (1999), 93–146 | DOI | MR | Zbl

[2] Yudovich V. I., “Nestatsionarnye techeniya idealnoi neszhimaemoi zhidkosti”, ZhVM i MF, 3:6 (1963), 1032–1066 | MR | Zbl

[3] Barbu V., Lasiecka I., Triggiani R., “Abstract setting of tangential boundary stabilization of Navier–Stokes equations by high-and low-gain feedback controllers”, Nonlinear Analysis, 64:12 (2006), 2704–2746 | DOI | MR | Zbl

[4] Coron J. M., “On null asymptotic stabilization of the two-dimensional incompressible Euler equations in a simply connected domains”, SIAM J. Control Optim., 37:6 (1999), 1874–1896 | DOI | MR | Zbl

[5] Coron J. M., Control and Nonlinearity, Math. Surv. Monographs, 136, Amer. Math. Soc., Providence, 2007 | MR | Zbl

[6] Fursikov A. V., “Stabilization for the 3D Navier-Stokes system by feedback boundary control”, Discrete Contin. Dynam. Syst., 10:1–2 (2004), 289–314 | MR | Zbl

[7] Fursikov A. V., “The simplest semilinear parabolic equation of normal type”, Math. Control Related Fields, 2:2 (2012), 141–170 | DOI | MR | Zbl

[8] Fursikov A. V., “On the normal semilinear parabolic equations corresponding to 3D Navier–Stokes system”, System Modeling and Optimization, 25th IFIP TC 7 Conf., CSMO 2011 (Berlin, Germany, September 12–16, 2011), Revised Selected Papers, IFIP Adv. Inform. Commun. Tech., 391, eds. D. Hömberg, F. Tröltzsch, Springer, Berlin, 2013, 338–347 | DOI | Zbl

[9] Fursikov A. V., “On one semilinear parabolic equation of normal type”, Mathematics and Life Sciences, De Gruyter Ser. Math. Life Sci., 1, De Gruyter, Berlin, 2013, 147–160 | MR

[10] Fursikov A. V., “On parabolic system of normal type corresponding to 3D Helmholtz system”, Amer. Math. Soc. Transl., 232 (2014), 99–118 | MR | Zbl

[11] Fursikov A. V., “Stabilization of the simplest normal parabolic equation”, Commun. Pure Appl. Analysis, 13:5 (2014), 1815–1854 | DOI | MR | Zbl

[12] Fursikov A. V., Gorshkov A. V., “Certain questions of feedback stabilization for Navier–Stokes equations”, Evolution Equations Control Theory, 1:1 (2012), 109–140 | DOI | MR | Zbl

[13] Fursikov A. V., Kornev A. A., “Feedback stabilization for Navier-Stokes equations: theory and calculations”, Mathematical Aspects of Fluid Mechanics, LMS Lect. Notes Ser., 402, Cambridge Univ. Press, Cambridge, 2012, 130–172 | MR | Zbl

[14] Krstic M., “On global stabilization of Burgers' equation by boundary control”, Systems Control Lett., 37 (1999), 123–141 | DOI | MR | Zbl

[15] Raymond J.-P., “Feedback boundary stabilization of the three-dimensional incompressible Navier–Stokes equations”, J. Math. Pures Appl., 87:6 (2007), 627–669 | DOI | MR | Zbl

[16] Tucsnk M., Weiss G., Observation and Control for Operator Semigroups, Birkhäuser, Berlin, 2009 | MR