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Article Dans Une Revue Journal of Mathematical Analysis and Applications Année : 2021

On the summability of the solutions of the inhomogeneous heat equation with a power-law nonlinearity and variable coefficients

Pascal Remy

Résumé

In this article, we investigate the summability of the formal power series solutions in time of the inhomogeneous heat equation with a power-law nonlinearity of degree two, and with variable coefficients. In particular, we give necessary and sufficient conditions for the 1-summability of the solutions in a given direction. These conditions generalize the ones given for the linear heat equation by W. Balser and M. Loday-Richaud in a 2009 article [5].
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hal-03993033 , version 1 (05-04-2023)

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Pascal Remy. On the summability of the solutions of the inhomogeneous heat equation with a power-law nonlinearity and variable coefficients. Journal of Mathematical Analysis and Applications, 2021, 494 (2), ⟨10.1016/j.jmaa.2020.124656⟩. ⟨hal-03993033⟩

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