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

Zhuangchu Luo; Hua Chen; Changgui Zhang

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

Analysis of PDEs 2012-02-22 v1

Authors: Zhuangchu Luo , Hua Chen , Changgui Zhang

Abstract

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.

Keywords

Nagumo norm Gevrey asymptotics summability singular PDEs formal solutions degenerated equations

Cite

@article{arxiv.1102.1158,
  title  = {Exponential type Nagumo norms and summability of formal solutions of singular partial differential equations},
  author = {Zhuangchu Luo and Hua Chen and Changgui Zhang},
  journal= {arXiv preprint arXiv:1102.1158},
  year   = {2012}
}

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