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Article Dans Une Revue RACSAM. Real Academia de Ciencias. Serie A, Matemáticas - Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A, Matemáticas Année : 2021

Gevrey regularity of the solutions of the inhomogeneous partial differential equations with a polynomial semilinearity

Résumé

In this article, we are interested in the Gevrey properties of the formal power series solution in time of the partial differential equations with a polynomial semilinearity and with analytic coefficients at the origin of Cn+1. We prove in particular that the inhomogeneity of the equation and the formal solution are together s-Gevrey for any s≥ sc, where sc is a nonnegative rational number fully determined by the Newton polygon of the associated linear PDE. In the opposite case s< sc, we show that the solution is generically sc-Gevrey while the inhomogeneity is s-Gevrey, and we give an explicit example in which the solution is s′-Gevrey for no s′< sc.
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Dates et versions

hal-03288061 , version 1 (22-10-2021)

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Citer

Pascal Remy. Gevrey regularity of the solutions of the inhomogeneous partial differential equations with a polynomial semilinearity. RACSAM. Real Academia de Ciencias. Serie A, Matemáticas - Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A, Matemáticas, 2021, 115 (3), ⟨10.1007/s13398-021-01085-5⟩. ⟨hal-03288061⟩
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