ON THE SUMMABILITY OF THE SOLUTIONS OF THE INHOMOGENEOUS HEAT EQUATION WITH A POWER-LAW NONLINEARITY AND VARIABLE COEFFICIENTS - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2020

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-02906351 , version 1 (24-07-2020)

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  • HAL Id : hal-02906351 , version 1

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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. 2020. ⟨hal-02906351⟩

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