Geodesic
The maximal nonuniqueness classes of solutions to the Cauchy problem for linear equations
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 9 (2010), pp. 90-93 Cet article a éte moissonné depuis la source Math-Net.Ru

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We study linear partial differential equations with increasing coefficients in a half-plane. We establish maximal nonuniqueness classes of solutions to the Cauchy problem for these equations. The proof is based on a new estimation method for a solution to the dual differential equation with a parameter.
Keywords: classes of uniqueness and nonuniqueness, Newton's diagram, Cauchy problem. 
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     author = {D. V. Turtin},
     title = {The maximal nonuniqueness classes of solutions to the {Cauchy} problem for linear equations},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
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     url = {http://geodesic.mathdoc.fr/item/IVM_2010_9_a9/}
}
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D. V. Turtin. The maximal nonuniqueness classes of solutions to the Cauchy problem for linear equations. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 9 (2010), pp. 90-93. http://geodesic.mathdoc.fr/item/IVM_2010_9_a9/

[1] Chebotarev N. G., Teoriya algebraicheskikh funktsii, Gostekhizdat, M., 1948

[2] Kosarev N. G., “O edinstvennosti resheniya zadachi Koshi dlya lineinykh uravnenii s peremennymi koeffitsientami”, Kachestvennye i priblizhennye metody issledovaniya operatornykh uravnenii, 2, Yaroslavl, 1977, 141–158 | MR | Zbl

[3] Gelfand I. M., Shilov G. E., Obobschennye funktsii. Nekotorye voprosy teorii differentsialnykh uravnenii, Fizmatlit, M., 1958 | MR

[4] Zhitomirskii Ya. I., “Klassy edinstvennosti resheniya zadachi Koshi dlya lineinykh uravnenii s rastuschimi koeffitsientami”, Izv. AN SSSR. Ser. matem., 31:4 (1967), 763–782 | MR | Zbl

[5] Kosarev N. G., “O zadache Koshi dlya lineinykh uravnenii s peremennymi koeffitsientami”, Nauchnye trudy IvGU. Matematika, 2, Ivanovo, 1999, 86–92

[6] Zolotarev G. N., “Netrivialnye resheniya zadachi Koshi s nulevymi nachalnymi usloviyami”, Uchen. zap. Ivanovsk. gos. ped. in-ta, 31 (1963), 29–36 | MR