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Izv. Akad. Nauk SSSR Ser. Mat., 1967, Volume 31, Issue 5, Pages 1159–1178 (Mi izv2581)  

This article is cited in 6 scientific papers (total in 6 papers)

Uniqueness classes for solutions of the Cauchy problem for linear equations with rapidly increasing coefficients

Ya. I. Zhitomirskii


Abstract: 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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English version:
Mathematics of the USSR-Izvestiya, 1967, 1:5, 1109–1129

Bibliographic databases:

UDC: 517.944
MSC: 34A12, 34Exx, 35A05
Received: 01.12.1966

Citation: Ya. I. Zhitomirskii, “Uniqueness classes for solutions of the Cauchy problem for linear equations with rapidly increasing coefficients”, Izv. Akad. Nauk SSSR Ser. Mat., 31:5 (1967), 1159–1178; Math. USSR-Izv., 1:5 (1967), 1109–1129

Citation in format AMSBIB
\Bibitem{Zhi67}
\by Ya.~I.~Zhitomirskii
\paper Uniqueness classes for solutions of the Cauchy problem for linear
equations with rapidly increasing coefficients
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1967
\vol 31
\issue 5
\pages 1159--1178
\mathnet{http://mi.mathnet.ru/izv2581}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=222486}
\zmath{https://zbmath.org/?q=an:0161.29505|0174.14801}
\transl
\jour Math. USSR-Izv.
\yr 1967
\vol 1
\issue 5
\pages 1109--1129
\crossref{https://doi.org/10.1070/IM1967v001n05ABEH000604}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Ya. I. Zhitomirskii, “On differential operators of infinite order in spaces of type $S$”, Math. USSR-Sb., 9:3 (1969), 379–388  mathnet  crossref  mathscinet  zmath
    2. V. P. Palamodov, “The work of G. E. Shilov in the theory of generalized functions and differential equations”, Russian Math. Surveys, 33:4 (1978), 219–235  mathnet  crossref  mathscinet  zmath
    3. O. A. Oleinik, E. V. Radkevich, “The method of introducing a parameter in the study of evolutionary equations”, Russian Math. Surveys, 33:5 (1978), 7–84  mathnet  crossref  mathscinet  zmath
    4. A. S. Kalashnikov, “Classes of uniqueness for integrodifferential equations with volterra operators of convolution type”, Funct. Anal. Appl., 13:2 (1979), 143–144  mathnet  crossref  mathscinet  zmath
    5. V. F. Vil'danova, F. Kh. Mukminov, “Anisotropic uniqueness classes for a degenerate parabolic equation”, Sb. Math., 204:11 (2013), 1584–1597  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    6. V. F. Vil'danova, F. Kh. Mukminov, “Täcklind uniqueness classes for heat equation on noncompact Riemannian manifolds”, Ufa Math. J., 7:2 (2015), 55–63  mathnet  crossref  isi  elib
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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