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 |
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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 |

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 |

Date Deposited: | 2021. Nov. 15. 15:56 |

Last Modified: | 2021. Nov. 15. 15:56 |

URI: | http://acta.bibl.u-szeged.hu/id/eprint/73921 |

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