Geodesic
Correctly solvable boundary value problems in an~infinite layer for systems of linear partial differential equations
Izvestiya. Mathematics , Tome 5 (1971) no. 1, pp. 193-210.

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We study classes of correct solvability of boundary value problems for systems of linear equations with constant coefficients of the form $\frac{\partial\bar u(x,t)}{\partial t}=P\bigl(\frac\partial{\partial x}\bigr)\bar u(x,t)$ in the layer $R^m\times[0,T]$ with boundary conditions consisting in prescribing certain components of the vectors $\bar u(x,0)$ and $\bar u (x,T)$ for $x\in R^m$. 
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V. M. Borok. Correctly solvable boundary value problems in an~infinite layer for systems of linear partial differential equations. Izvestiya. Mathematics , Tome 5 (1971) no. 1, pp. 193-210. http://geodesic.mathdoc.fr/item/IM2_1971_5_1_a10/

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