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Stabilization of a Solution to the Heat Equation with Boundary Control in the Exterior of a Disc

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We study the stabilization of a solution to the heat equation with boundary control in the exterior of a disc. For any given k > 0 we construct a boundary control stabilizing the solution to zero with rate 1/tk. Bibliography: 5 titles.

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References

  1. A. V. Gorshkov, “Stabilizing a solution of the 2D Navier-Stokes system in the exterior of a bounded domain by means of a control on the boundary” [in Russian], Mat. Sb. 203, No, 9, 15–40 (2012); English transl.: Sb. Math. 203, No, 9, 1244–1268 (2012).

  2. M. S. Agranovich and M. I. Vishik, “Elliptic problems with a parameter and parabolic problems of general type” [in Russian], Usp. Mat. Nauk 19, No. 3, 53–161 (1964); English transl.: Russ. Math. Surv. 19, No. 3, 53–157 (1964).

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Correspondence to A. V. Gorshkov.

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Translated from Problemy Matematicheskogo Analiza 82, September 2015, pp. 71-81.

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Gorshkov, A.V. Stabilization of a Solution to the Heat Equation with Boundary Control in the Exterior of a Disc. J Math Sci 210, 635–647 (2015). https://doi.org/10.1007/s10958-015-2582-3

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  • DOI: https://doi.org/10.1007/s10958-015-2582-3

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