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Exponential-type Nagumo norms and summability of formal solutions of singular partial differential equations

Zhuangchu LuoHua ChenChanggui Zhang — 2012

Annales de l’institut Fourier

In this paper, we study a class of first order nonlinear degenerate partial differential equations with singularity at ( t , x ) = ( 0 , 0 ) C 2 . Using exponential-type Nagumo norm approach, the Gevrey asymptotic analysis is extended to case of holomorphic parameters in a natural way. A sharp condition is then established to deduce the k -summability of the formal solutions. Furthermore, analytical solutions in conical domains are found for each type of these nonlinear singular PDEs.

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