Geodesic
Uniqueness classes for solutions of the Cauchy problem for linear
Izvestiya. Mathematics, Tome 1 (1967) no. 5, pp. 1109-1129
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Uniqueness classes, and also nonuniqueness classes, are found for solutions of the Cauchy problem for equations or the form $\displaystyle\frac{\partial u}{\partial t}=\sum^n_{k=0}q_k(x)\frac{\partial^ku}{\partial x^k}$ in which the growth $q_0(x)$ as $|x|\to\infty$ is sufficiently rapid, the growth of the other coefficients is “subordinate” to that of $q_0(x)$, and the classes depend on $q_0(x)$. 
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Ya. I. Zhitomirskii. Uniqueness classes for solutions of the Cauchy problem for linear. Izvestiya. Mathematics, Tome 1 (1967) no. 5, pp. 1109-1129. http://geodesic.mathdoc.fr/item/IM2_1967_1_5_a11/

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