Gevrey index theorem for some inhomogeneous semilinear partial differential equations with variable coefficients

Pascal Remy (1)

1 LMV - Laboratoire de Mathématiques de Versailles

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

Mots clés: Gevrey order; Inhomogeneous partial differential equation; Nonlinear partial differential equation; Newton polygon; Formal power series; Divergent power series

Domaines: Systèmes dynamiques [math.DS]

Pascal Remy. Gevrey index theorem for some inhomogeneous semilinear partial differential equations with variable coefficients. 2019. ⟨hal-02263353⟩