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J. Sib. Fed. Univ. Math. Phys., 2009, Volume 2, Issue 3, Pages 258–270 (Mi jsfu72)  

This article is cited in 3 scientific papers (total in 3 papers)

On Estimates of Solutions of the Split Problems for Some Multi-Dimensional Partial Differential Equations

Yuri Ya. Belov

Institute of Mathematics, Siberian Federal University, Krasnoyarsk, Russia

Abstract: We consider multidimensional second order parabolic equations and the first order partial differential equations. We consider various splittings of the Cauchy problem in the case when the coefficients of the equation depending on time and all space variables and have a special form. The uniform correctness of the split problems, that is, a sufficient condition for the split problems solutions convergence to the solutions to the original problems and the uniform correctness of this problem is proved in classes of smooth functions.

Keywords: differential equation, Cauchy problem, split, stability, convergence.

Full text: PDF file (183 kB)
References: PDF file   HTML file
UDC: 517.9
Received: 10.05.2009
Received in revised form: 10.06.2009
Accepted: 20.06.2009
Language:

Citation: Yuri Ya. Belov, “On Estimates of Solutions of the Split Problems for Some Multi-Dimensional Partial Differential Equations”, J. Sib. Fed. Univ. Math. Phys., 2:3 (2009), 258–270

Citation in format AMSBIB
\Bibitem{Bel09}
\by Yuri~Ya.~Belov
\paper On Estimates of Solutions of the Split Problems for Some Multi-Dimensional Partial Differential Equations
\jour J. Sib. Fed. Univ. Math. Phys.
\yr 2009
\vol 2
\issue 3
\pages 258--270
\mathnet{http://mi.mathnet.ru/jsfu72}


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    This publication is cited in the following articles:
    1. S. V. Polyntseva, V. V. Sosedov, “Zadacha opredeleniya koeffitsientov pri proizvodnoi po vremeni i starshei proizvodnoi po prostranstvennoi peremennoi v parabolicheskom uravnenii”, Trudy sedmoi Vserossiiskoi nauchnoi konferentsii s mezhdunarodnym uchastiem (3–6 iyunya 2010 g.). Chast 3, Differentsialnye uravneniya i kraevye zadachi, Matem. modelirovanie i kraev. zadachi, Samarskii gosudarstvennyi tekhnicheskii universitet, Samara, 2010, 246–248  mathnet
    2. Ekaterina N. Kriger, Igor V. Frolenkov, “An identification problem of nonlinear lowest term coefficient in the special form for two-dimensional semilinear parabolic equation”, Zhurn. SFU. Ser. Matem. i fiz., 9:2 (2016), 180–191  mathnet  crossref
    3. Yuri Ya. Belov, Kirill V. Korshun, “On rate of convergence of Tonelli's and weak approximation methods for loaded equations”, Zhurn. SFU. Ser. Matem. i fiz., 11:3 (2018), 286–294  mathnet  crossref
  • Журнал Сибирского федерального университета. Серия "Математика и физика"
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