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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,
u(x,0)=u_0(x),\qquad u(x,T)=u_T(x) \end{gather*}
($x\in R_m$, $t\in[0,T]$; $P(s)$ 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
Received: 28.01.1970

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}


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  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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