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Removable singularities of solutions of nonlinear singular partial differential equations

Hidetoshi Tahara — 1996

Banach Center Publications

1. Introduction. The study of singularities has been one of the main subjects of research in partial differential equations. In the case of linear equations the singularities are now pretty well understood; but in the nonlinear case there seems to be still very few studies. In this paper I want to discuss the singularities of solutions of a class of nonlinear singular partial differential equations in the complex domain. The class is only a model, but it helps one understand that the situation in...

Maillet type theorem and Gevrey regularity in time of solutions to nonlinear partial differential equations

Hidetoshi Tahara — 2012

Banach Center Publications

Formal solutions of nonlinear first order totally characteristic type PDE with irregular singularity

Hua Chen; Zhuangchu Luo; Hidetoshi Tahara — 2001

Annales de l’institut Fourier

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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Currently displaying 1 – 3 of 3

Removable singularities of solutions of nonlinear singular partial differential equations

Maillet type theorem and Gevrey regularity in time of solutions to nonlinear partial differential equations

Formal solutions of nonlinear first order totally characteristic type PDE with irregular singularity