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Exponential-type Nagumo norms and summability of formal solutions of singular partial differential equations. (English. French summary) Zbl 1252.30025
Authors’ abstract: In this paper, we study a class of first order nonlinear degenerate partial differential equations with singularity at \((t,x)=(0,0)\in {\mathbb C}^2\). 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.

MSC:
30E15 Asymptotic representations in the complex plane
32D15 Continuation of analytic objects in several complex variables
35C10 Series solutions to PDEs
35C20 Asymptotic expansions of solutions to PDEs
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