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On the problem of determining the parameter of a parabolic equation

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Abstract

We study the boundary-value problem of determining the parameter p of a parabolic equation

$$ v^{\prime}(t) + Av(t) = f(t) + p,\quad 0 \leqslant t \leqslant 1,\quad v(0) = \varphi, \quad v(1) = \psi, $$

with strongly positive operator A in an arbitrary Banach space E. The exact estimates are established for the solution of this problem in Hölder norms. In applications, the exact estimates are obtained for the solutions of the boundary-value problems for parabolic equations.

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Authors and Affiliations

  1. Fatih University, Istanbul, Turkey

    A. Ashyralyev

  2. ITTU, Ashgabat, Turkmenistan

    A. Ashyralyev

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  1. A. Ashyralyev
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 62, No. 9, pp. 1200–1210, September, 2010.

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Ashyralyev, A. On the problem of determining the parameter of a parabolic equation. Ukr Math J 62, 1397–1408 (2011). https://doi.org/10.1007/s11253-011-0438-7

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  • DOI: https://doi.org/10.1007/s11253-011-0438-7

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