Gevrey Order of Formal Power Series Solutions of Inhomogeneous Partial Differential Equations with Constant Coefficients

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概要

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• In an earlier paper, the first author showed that certain normalized formal solutions of homogeneous linear partial differential equations with constant coefficients are multisummable, with a multisummability type that can be determined from a Newton polygon associated with the PDE. In this article, some of the results obtained there are extended in several directions: First of all, arbitrary formal solutions of inhomogeous PDE are considered, and it is shown that, in some sense, they can be computed completely explicitly. Secondly, the Gevrey order of these formal solutions is determined. Finally, formal power series are discussed that, in general, do not satisfy a PDE with constant coefficients, but instead may be considered as solutions of singularly perturbed ODE, or integro-differential equations of a certain form.

• 日本数学会函数方程式論分科会の論文

著者

• YOSHINO MASAFUMI

  Hiroshima University

• Balser Werner

  Universität Ulm

関連論文

• Smooth-integrable and analytic-nonintegrable resonant Hamiltonians (Recent development of micro-local analysis for the theory of asymptotic analysis)
• Gevrey Order of Formal Power Series Solutions of Inhomogeneous Partial Differential Equations with Constant Coefficients

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