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Izv. Akad. Nauk SSSR Ser. Mat., 1973, Volume 37, Issue 3, Pages 676–690 (Mi izv2286)  

An investigation of the behavior of $L_2$-norms of the solutions of strongly parabolic systems with dissipation

S. D. Èidel'man, F. O. Porper


Abstract: It is established under certain interrelations between the growth of the initial function and the dissipation intensity that an increasing solution becomes with the passage of time a bounded and ultimately decreasing function of the spatial coordinates. The behavior of $L_2$-norms (containing weights depending in a special manner on the time $t$) of the solutions is investigated for this purpose. The results are essentially based on inequalities established in the paper between the norms and quasinorms introduced and which, in our view, are of independent interest.

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English version:
Mathematics of the USSR-Izvestiya, 1973, 7:3, 675–689

Bibliographic databases:

UDC: 517.9
MSC: Primary 35B35, 35K45; Secondary 35C15
Received: 03.12.1970

Citation: S. D. Èidel'man, F. O. Porper, “An investigation of the behavior of $L_2$-norms of the solutions of strongly parabolic systems with dissipation”, Izv. Akad. Nauk SSSR Ser. Mat., 37:3 (1973), 676–690; Math. USSR-Izv., 7:3 (1973), 675–689

Citation in format AMSBIB
\Bibitem{EidPor73}
\by S.~D.~\`Eidel'man, F.~O.~Porper
\paper An investigation of the behavior of $L_2$-norms of the solutions of strongly parabolic systems with dissipation
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1973
\vol 37
\issue 3
\pages 676--690
\mathnet{http://mi.mathnet.ru/izv2286}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=340822}
\zmath{https://zbmath.org/?q=an:0277.35063}
\transl
\jour Math. USSR-Izv.
\yr 1973
\vol 7
\issue 3
\pages 675--689
\crossref{https://doi.org/10.1070/IM1973v007n03ABEH001970}


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  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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