Gevrey index theorem for the inhomogeneous n-dimensional heat equation with a power-law nonlinearity and variable coefficients

We are interested in the Gevrey properties of the formal power series solution in time of the inhomogeneous semilinear heat equation with a powerlaw nonlinearity in 1-dimensional time variable t ∈ C and n-dimensional spatial variable x ∈ C n and with analytic initial condition and analytic coefficie...

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Bibliographic Details
Main Author: Remy Pascal
Format: Article
Published: 2021
Series:Acta scientiarum mathematicarum 87 No. 1-2
Kulcsszavak:Matematika
doi:10.14232/actasm-020-571-9

Online Access:http://acta.bibl.u-szeged.hu/73921
Description
Summary:We are interested in the Gevrey properties of the formal power series solution in time of the inhomogeneous semilinear heat equation with a powerlaw nonlinearity in 1-dimensional time variable t ∈ C and n-dimensional spatial variable x ∈ C n and with analytic initial condition and analytic coefficients at the origin x = 0. We prove in particular that the inhomogeneity of the equation and the formal solution are together s-Gevrey for any s ≥ 1. In the opposite case s < 1, we show that the solution is generically 1-Gevrey while the inhomogeneity is s-Gevrey, and we give an explicit example in which the solution is s -Gevrey for no s ′ < 1.
Physical Description:163-181
ISSN:2064-8316