Geodesic
On correct solvability of a~boundary value problem in an infinite slab for linear equations with constant coefficients
Izvestiya. Mathematics , Tome 5 (1971) no. 4, pp. 935-953.

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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\left(\frac\partial{\partial x}\right)\frac{\partial u(x,t)}{\partial t}+Q\left(\frac\partial{\partial x}\right)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 $s_1,\dots,s_m$ with constant coefficients) in various classes of functions. 
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     title = {On correct solvability of a~boundary value problem in an infinite slab for linear equations with constant coefficients},
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V. M. Borok. On correct solvability of a~boundary value problem in an infinite slab for linear equations with constant coefficients. Izvestiya. Mathematics , Tome 5 (1971) no. 4, pp. 935-953. http://geodesic.mathdoc.fr/item/IM2_1971_5_4_a10/

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