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arXiv · 1102.1158

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

Zhuangchu Luo·Hua Chen·Changgui Zhang
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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.

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Zhuangchu Luo, Hua Chen, Changgui Zhang. 2011-02-06. Exponential type Nagumo norms and summability of formal solutions of singular partial differential equations. https://arxiv.org/abs/1102.1158

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