Geodesic
Uniqueness classes for solutions of the Cauchy problem for linear
Izvestiya. Mathematics, Tome 1 (1967) no. 5, pp. 1109-1129 
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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Voir la notice de l'article provenant de la source Math-Net.Ru

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 $q_0(x)$.

[1] Zhitomirskii Ya. I., “Klassy edinstvennosti resheniya zadachi Koshi dlya lineinykh uravnenii s rastuschimi koeffitsientami”, Izv. AN SSSR. Ser. matem., 31 (1967), 763–782 | Zbl

[2] Zhitomirskii Ya. I., “Klassy edinstvennosti resheniya zadachi Koshi dlya lineinykh uravnenii s bystro rastuschimi koeffitsientami”, Dokl. AN SSSR, 173:1 (1967), 26–29 | Zbl

[3] Rapoport I. M., O nekotorykh asimptoticheskikh metodakh v teorii differentsialnykh uravnenii, AN USSR, 1954

[4] Mandelbroit S., Primykayuschie ryady. Regulyarizatsii posledovatelnostei. Primeneniya, IL, M., 1955

[5] Zhitomirskii Ya. I., “Tochnye klassy edinstvennosti resheniya zadachi Koshi dlya uravnenii vtorogo poryadka”, Dokl. AN SSSR, 171:1 (1966), 29–32 | Zbl