On the Convergence of Formal Solutions of a System of Partial Differential Equations
Authors:
S. P. Chulkov
Affiliation:
(1) Lomonosov Moscow State University, Moscow, Russia;(2) Independent University of Moscow, Moscow, Russia
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.”