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Funktsional. Anal. i Prilozhen., 2005, Volume 39, Issue 3, Pages 64–75 (Mi faa75)  

This article is cited in 1 scientific paper (total in 1 paper)

On the Convergence of Formal Solutions of a System of Partial Differential Equations

S. P. Chulkovab

a M. V. Lomonosov Moscow State University
b Independent University of Moscow

Abstract: We study a version of the classical problem on the convergence of formal solutions of systems of partial differential equations. A necessary and sufficient condition for the convergence of a given formal solution (found by any method) is proved. This convergence criterion applies to systems of partial differential equations (possibly, nonlinear) solved for the highest-order derivatives or, which is most important, “almost solved for the highest-order derivatives.”

Keywords: systems of partial differential equations, convergence of formal solutions, ordered semigroup $\mathbb{Z}^n_{\geqslant 0}$, system of partial differential equations solved for the highest-order derivatives, system of partial differential equations “almost solved for the highest-order derivatives”

DOI: https://doi.org/10.4213/faa75

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English version:
Functional Analysis and Its Applications, 2005, 39:3, 215–224

Bibliographic databases:

UDC: 517.95
Received: 01.09.2003

Citation: S. P. Chulkov, “On the Convergence of Formal Solutions of a System of Partial Differential Equations”, Funktsional. Anal. i Prilozhen., 39:3 (2005), 64–75; Funct. Anal. Appl., 39:3 (2005), 215–224

Citation in format AMSBIB
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\paper On the Convergence of Formal Solutions of a System of Partial Differential Equations
\jour Funktsional. Anal. i Prilozhen.
\yr 2005
\vol 39
\issue 3
\pages 64--75
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\yr 2005
\vol 39
\issue 3
\pages 215--224
\crossref{https://doi.org/10.1007/s10688-005-0040-6}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. Vershynina, S. L. Gefter, “On analytic solutions of the heat equation with an operator coefficient”, J. Math. Sci. (N. Y.), 156:5 (2009), 799–812  mathnet  crossref  zmath  elib
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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