This article is cited in 2 papers

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

S. P. Chulkov<sup>ab

a</sup> 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”.

UDC: 517.95

Received: 01.09.2003

DOI: 10.4213/faa75

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

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