Geodesic
On the Convergence of Formal Solutions of a System of Partial Differential Equations
Funkcionalʹnyj analiz i ego priloženiâ, Tome 39 (2005) no. 3, pp. 64-75

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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, 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”.
Mots-clés : convergence of formal solutions 
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     author = {S. P. Chulkov},
     title = {On the {Convergence} of {Formal} {Solutions} of a {System} of {Partial} {Differential} {Equations}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
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     url = {http://geodesic.mathdoc.fr/item/FAA_2005_39_3_a5/}
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S. P. Chulkov. On the Convergence of Formal Solutions of a System of Partial Differential Equations. Funkcionalʹnyj analiz i ego priloženiâ, Tome 39 (2005) no. 3, pp. 64-75. http://geodesic.mathdoc.fr/item/FAA_2005_39_3_a5/