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Article Dans Une Revue Acta Scientiarum Mathematicarum Année : 2021

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

Résumé

We are interested in the Gevrey properties of the formal power series solution in time of the inhomogeneous semilinear heat equation with a power-law nonlinearity in 1-dimensional time variable t ∈ C and n-dimensional spatial variable x ∈ Cn 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.
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hal-03993039 , version 1 (16-02-2023)

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Pascal Remy. Gevrey index theorem for the inhomogeneous n-dimensional heat equation with a power-law nonlinearity and variable coefficients. Acta Scientiarum Mathematicarum, 2021, 87 (1), pp.163-181. ⟨10.14232/actasm-020-571-9⟩. ⟨hal-03993039⟩

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