Abstract:
In the paper the second boundary value problem for the third order composite type equations is investigated. We established Saint-Venant's type energy estimates for weak solutions of the problem on Sobolev classes. The obtained estimates are used to prove uniqueness theorems in the classes of functions growing at infinity. These uniqueness classes depend on the geometrical characteristics of the domain. Moreover, energy estimates allowing us to investigate behavior of solution in the neighborhood of singular points were obtained.
Keywords:
uniqueness theorem, Saint-Venant's principle, third order differential equations, singular points, general solutions, unbounded domains.
Original article submitted 09/I/2011 revision submitted – 04/III/2012
Citation:
A. R. Khashimov, “On uniqueness of the second boundary value problem solutions for the third order composite type equation in unbounded domains”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2(27) (2012), 18–25
\Bibitem{Kha12}
\by A.~R.~Khashimov
\paper On uniqueness of the second boundary value problem solutions for the third order composite type equation in unbounded domains
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2012
\vol 2(27)
\pages 18--25
\mathnet{http://mi.mathnet.ru/vsgtu912}
\crossref{https://doi.org/10.14498/vsgtu912}
\zmath{https://zbmath.org/?q=an:1326.35213}
Linking options:
https://www.mathnet.ru/eng/vsgtu912
https://www.mathnet.ru/eng/vsgtu/v127/p18
This publication is cited in the following 1 articles:
V Boyarinov, V Davidenko, A Moryakov, “NOT STATIONARY BSS-6 DIFFUSION TEST IN TRANSPORT INTERPRETATION”, PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. SERIES: NUCLEAR AND REACTOR CONSTANTS, 2019:2 (2019), 49
Citation in format AMSBIB
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