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Funktsional'nyi Analiz i ego Prilozheniya, 2005, Volume 39, Issue 3, Pages 64–75
DOI: https://doi.org/10.4213/faa75 (Mi faa75) 		 
This article is cited in 2 scientific papers (total in 2 papers)

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
Full-text PDF (207 kB) Citations (2)
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DOI: https://doi.org/10.4213/faa75
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”.
Received: 01.09.2003
English version:
Functional Analysis and Its Applications, 2005, Volume 39, Issue 3, Pages 215–224
DOI: https://doi.org/10.1007/s10688-005-0040-6
Bibliographic databases:
Document Type: Article
UDC: 517.95
Language: Russian
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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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Функциональный анализ и его приложения Functional Analysis and Its Applications
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