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Izv. Akad. Nauk SSSR Ser. Mat., 1969, Volume 33, Issue 2, Pages 368–378 (Mi izv2134)  

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

The stabilization of solutions of the neralized Cauchy problem for ultraparabolic equations

Yu. N. Drozhzhinov


Abstract: By using an “integral” representation of the solution of the generalized Cauchy problem for ultraparabolic equations, a necessary and sufficient condition for the stabilization of the solution has been obtained for the class of positive initial functionals. In the class of “bounded with respect to translation” functionals, it has been proved that a necessary and sufficient condition for the stabilization of the solution in a weak sense is the existence of a generalized spherical limiting mean.

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English version:
Mathematics of the USSR-Izvestiya, 1969, 3:2, 345–355

Bibliographic databases:

UDC: 517.9
MSC: 35B35, 35K70
Received: 24.01.1968

Citation: Yu. N. Drozhzhinov, “The stabilization of solutions of the neralized Cauchy problem for ultraparabolic equations”, Izv. Akad. Nauk SSSR Ser. Mat., 33:2 (1969), 368–378; Math. USSR-Izv., 3:2 (1969), 345–355

Citation in format AMSBIB
\Bibitem{Dro69}
\by Yu.~N.~Drozhzhinov
\paper The stabilization of solutions of the neralized Cauchy problem for ultraparabolic equations
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1969
\vol 33
\issue 2
\pages 368--378
\mathnet{http://mi.mathnet.ru/izv2134}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=276618}
\zmath{https://zbmath.org/?q=an:0179.14802|0196.12202}
\transl
\jour Math. USSR-Izv.
\yr 1969
\vol 3
\issue 2
\pages 345--355
\crossref{https://doi.org/10.1070/IM1969v003n02ABEH000768}


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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. A. K. Gushchin, “On the uniform stabilization of solutions of the second mixed problem for a parabolic equation”, Math. USSR-Sb., 47:2 (1984), 439–498  mathnet  crossref  mathscinet  zmath
    2. S. A. Tersenov, “On boundary value problems for a class of ultraparabolic equations, and their applications”, Math. USSR-Sb., 61:2 (1988), 529–544  mathnet  crossref  mathscinet  zmath
    3. F. Kh. Mukminov, “On uniform stabilization of solutions of the first mixed problem for a parabolic equation”, Math. USSR-Sb., 71:2 (1992), 331–353  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    4. F. Kh. Mukminov, “On uniform stabilization of solutions of the exterior problem for the Navier–Stokes equations”, Russian Acad. Sci. Sb. Math., 81:2 (1995), 297–320  mathnet  crossref  mathscinet  zmath  isi
    5. V. N. Denisov, “On the behaviour of solutions of parabolic equations for large values of time”, Russian Math. Surveys, 60:4 (2005), 721–790  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    6. V. A. Litovchenko, I. M. Dovzhytska, “Stabilization of solutions to Shilov-type parabolic systems with nonnegative genus”, Siberian Math. J., 55:2 (2014), 276–283  mathnet  crossref  mathscinet  isi
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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