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

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

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
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
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
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
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
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
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