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 Izv. Akad. Nauk SSSR Ser. Mat., 1971, Volume 35, Issue 4, Pages 922–939 (Mi izv2084)

On correct solvability of a boundary value problem in an infinite slab for linear equations with constant coefficients

V. M. Borok

Abstract: Conditions depending on the properties of the polynomials $P(s)$ and $Q(s)$ are found for the correct solvability of the boundary value problem
\begin{gather*} \frac{\partial^2u(x,t)}{\partial t^2}+P(\frac\partial{\partial x})\frac{\partial u(x,t)}{\partial t}+Q(\frac\partial{\partial x})u(x,t)=0,
($x\in R_m$, $t\in[0,T]$; $P(s)$ and $Q(s)$ are polynomials in $s_1,…,s_m$ with constant coefficients) in various classes of functions.

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English version:
Mathematics of the USSR-Izvestiya, 1971, 5:4, 935–953

Bibliographic databases:

UDC: 517.94
MSC: Primary 35A05; Secondary 35G15

Citation: V. M. Borok, “On correct solvability of a boundary value problem in an infinite slab for linear equations with constant coefficients”, Izv. Akad. Nauk SSSR Ser. Mat., 35:4 (1971), 922–939; Math. USSR-Izv., 5:4 (1971), 935–953

Citation in format AMSBIB
\Bibitem{Bor71} \by V.~M.~Borok \paper On correct solvability of a~boundary value problem in an infinite slab for linear equations with constant coefficients \jour Izv. Akad. Nauk SSSR Ser. Mat. \yr 1971 \vol 35 \issue 4 \pages 922--939 \mathnet{http://mi.mathnet.ru/izv2084} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=289924} \zmath{https://zbmath.org/?q=an:0219.35015} \transl \jour Math. USSR-Izv. \yr 1971 \vol 5 \issue 4 \pages 935--953 \crossref{https://doi.org/10.1070/IM1971v005n04ABEH001126}