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

Remy Pascal: Gevrey index theorem for the inhomogeneous n-dimensional heat equation with a power-law nonlinearity and variable coefficients. In: Acta scientiarum mathematicarum, (87) 1-2. pp. 163-181. (2021)

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Abstract

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.

Item Type:	Article
Heading title:	Analysis
Journal or Publication Title:	Acta scientiarum mathematicarum
Date:	2021
Volume:	87
Number:	1-2
ISSN:	2064-8316
Page Range:	pp. 163-181
Language:	English
Publisher:	Bolyai Institute, University of Szeged
Place of Publication:	Szeged
Related URLs:	http://acta.bibl.u-szeged.hu/73791/
DOI:	10.14232/actasm-020-571-9
Uncontrolled Keywords:	Matematika
Additional Information:	Bibliogr.: p. 177-181. ; összefoglalás angol nyelven
Subjects:	01. Natural sciences 01. Natural sciences > 01.01. Mathematics
Date Deposited:	2021. Nov. 15. 15:56
Last Modified:	2026. Feb. 18. 13:37
URI:	http://acta.bibl.u-szeged.hu/id/eprint/73921

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