Pré-Publication, Document De Travail Année : 2019

GEVREY INDEX THEOREM FOR THE INHOMOGENEOUS n-DIMENSIONAL HEAT EQUATION WITH A POWER-LAW NONLINEARITY AND VARIABLE COEFFICIENTS

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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 $t\in\mathbb{C}$ and $n$-dimensional spatial variable $x\in\mathbb{C}^n$ 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 $s\geq1$. In the opposite case $s<1$, we show that the solution is $1$-Gevrey at most 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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Est référencée par hal-03993039 Article 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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hal-02117418 , version 1 (02-05-2019)

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Pascal Remy. GEVREY INDEX THEOREM FOR THE INHOMOGENEOUS n-DIMENSIONAL HEAT EQUATION WITH A POWER-LAW NONLINEARITY AND VARIABLE COEFFICIENTS. 2019. ⟨hal-02117418⟩
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