Existence of Gevrey approximate solutions for certain systems of linear vector fields applied to involutive systems of first-order nonlinear pdes

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• 作者：Rafael F. Barostichi^a ; ^{barostichi@dm.ufscar.br"" rel=""nofollow} ; Gerson Petronilho ; ^a ; ^{gerson@dm.ufscar.br"" rel=""nofollow}
• 关键词：Gevrey approximate solutions for a system ; Gevrey wave-front set ; System of nonlinear pde of first order
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2011
• 出版时间：1 October 2011
• 年：2011
• 卷：382
• 期：1
• 页码：248-260
• 全文大小：224 K

文摘

Given a G^s-involutive structure, , a Gevrey submanifold XM which is maximally real and a Gevrey function u₀ on X we construct a Gevrey function u which extends u₀ and is a Gevrey approximate solution for . We then use our construction to study Gevrey micro-local regularity of solutions, , of a system of nonlinear pdes of the form where F_j(x,ζ₀,ζ) are Gevrey functions of order s>1 and holomorphic in . The functions F_j satisfy an involutive condition and d_ζF₁d_ζF_n≠0.