Geodesic
On solutions of a parabolic equation that decrease with respect to the space variables
Sbornik. Mathematics, Tome 13 (1971) no. 1, pp. 1-11 Cet article a éte moissonné depuis la source Math-Net.Ru

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The equation $L(x,D)u(x)=0$ is considered, where the operator $L(x,D)$ in the region is representable in the form $L(x,D)=L_m(x,D)+L_0(x, D)$; here $L_m(x,D)$ has order $m$, real coefficients in $C^1$, contains derivatives in the variables $x_1,\dots,x_k$, $k, and is elliptic in these variables, and for any real vector $N=\{N_1,\dots,N_k\}\ne0$ the equation $L_m(x,\xi+i\tau N)=0$, $\xi=\{\xi_1,\dots,\xi_k\}$, for any real $\xi$ not proportional to $N$ does not have double real zeros $\tau$. Bibliography: 3 titles. 
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     title = {On solutions of a~parabolic equation that decrease with respect to the space variables},
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I. V. Kudryavtseva. On solutions of a parabolic equation that decrease with respect to the space variables. Sbornik. Mathematics, Tome 13 (1971) no. 1, pp. 1-11. http://geodesic.mathdoc.fr/item/SM_1971_13_1_a0/

[1] M. M. El Borai, “O korrektnosti zadachi Koshi”, Vestnik MGU, 14 (1968), 15–21 | MR

[2] L. Khermander, Lineinye differentsialnye operatory s chastnymi proizvodnymi, Mir, Moskva, 1965 | MR

[3] R. Ya. Glagoleva, “Nekotorye svoistva reshenii lineinogo parabolicheskogo uravneniya vtorogo poryadka”, Matem. sb., 74(116) (1967), 47–74 | Zbl