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
Document type :
Preprints, Working Papers, ...
Complete list of metadatas

Cited literature [62 references]  Display  Hide  Download

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

File

Gevrey_index_theorem_inhomogen...
Files produced by the author(s)

Identifiers

  • HAL Id : hal-02263353, version 1

Citation

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

Share

Metrics

Record views

7

Files downloads

17