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

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

2011-02-06

arxiv.org/abs/1102.1158v1

Ann. Inst. Fourier (Grenoble), 62 (2012)

Mathematics

Analysis of PDEs

Scientific paper

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

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