# GEVREY INDEX THEOREM FOR SOME INHOMOGENEOUS SEMILINEAR PARTIAL DIFFERENTIAL EQUATIONS WITH VARIABLE COEFFICIENTS

Abstract : In this article, we are interested in the Gevrey properties of the formal power series solution in time of some partial differential equations with a power-law nonlinearity and with analytic coefficients at the origin of $C^2$. We prove in particular that the inhomogeneity of the equation and the formal solution are together $s$-Gevrey for any $s\geq s_c$, where $s_c$ is a nonnegative rational number fully determined by the Newton polygon of the associated linear PDE. In the opposite case \$s
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https://hal.archives-ouvertes.fr/hal-02263353
Contributor : Pascal Remy <>
Submitted on : Sunday, August 4, 2019 - 2:34:31 PM
Last modification on : Wednesday, August 7, 2019 - 1:12:00 AM

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• HAL Id : hal-02263353, version 1

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Pascal Remy. GEVREY INDEX THEOREM FOR SOME INHOMOGENEOUS SEMILINEAR PARTIAL DIFFERENTIAL EQUATIONS WITH VARIABLE COEFFICIENTS. 2019. ⟨hal-02263353⟩

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