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 Eurasian Math. J., 2020, Volume 11, Number 1, Pages 95–100 (Mi emj359)

Short communications

Existence and maximal regularity of solutions in $L_2(\mathbb{R}^2)$ for a hyperbolic type differential equation with quickly growing coefficients

M. B. Muratbekova, Ye. N. Bayandiyevb

a Department of Higher Mathematics and Mathematics Teaching Methodology, Taraz State Pedagogical University, 62 Tole bi St, 080001 Taraz, Kazakhstan
b Department of Mechanics and Mathematics, L.N. Gumilyov Eurasian National University, 13 Munaitpasov St, 010008 Nur-Sultan, Kazakhstan

Abstract: In this paper the problem of the existence of solutions is studied for a hyperbolic type differential equation defined in an unbounded domain. The problem of the smoothness of solutions is also considered here. Such problems are of particular interest when the coefficients are unbounded. The novelty of the work is that the weighted coercive estimate is obtained for the solutions of a hyperbolic type differential equation with quickly growing coefficients.

Keywords and phrases: hyperbolic type equation, maximal regularity, an unbounded domain, nonsmooth coefficients.

 Funding Agency Grant Number Ministry of Education and Science of the Republic of Kazakhstan AP05131080 This work was supported by the Ministry of Education and Science of the Republic of Kazakhstan [grant number (IRN) AP05131080].

DOI: https://doi.org/10.32523/2077-9879-2020-11-1-95-100

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MSC: 35M10
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Citation: M. B. Muratbekov, Ye. N. Bayandiyev, “Existence and maximal regularity of solutions in $L_2(\mathbb{R}^2)$ for a hyperbolic type differential equation with quickly growing coefficients”, Eurasian Math. J., 11:1 (2020), 95–100

Citation in format AMSBIB
\Bibitem{MurBay20} \by M.~B.~Muratbekov, Ye.~N.~Bayandiyev \paper Existence and maximal regularity of solutions in $L_2(\mathbb{R}^2)$ for a hyperbolic type differential equation with quickly growing coefficients \jour Eurasian Math. J. \yr 2020 \vol 11 \issue 1 \pages 95--100 \mathnet{http://mi.mathnet.ru/emj359} \crossref{https://doi.org/10.32523/2077-9879-2020-11-1-95-100}