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In this paper, we study a class of first order nonlinear degenerate partial differential equations with singularity at . 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 -summability of the formal solutions. Furthermore, analytical solutions in conical domains are found for each type of these nonlinear singular PDEs.
In this paper, we calculate the formal Gevrey index of the formal solution of a class of
nonlinear first order totally characteristic type partial differential equations with
irregular singularity in the space variable. We also prove that our index is the best
possible one in a generic case.
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