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

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 solutio...

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Bibliographic Details
Published inJournal of mathematical analysis and applications Vol. 494; no. 2; p. 124656
Main Author Remy, Pascal
Format Journal Article
LanguageEnglish
Published Elsevier Inc 15.02.2021
Elsevier
Subjects
Analysis of PDEs
Divergent power series
Formal power series
Heat equation
Inhomogeneous partial differential equation
Mathematics
Nonlinear partial differential equation
Summability
Formal power series
Summability
Inhomogeneous partial differential equation
Nonlinear partial differential equation
Divergent power series
Heat equation
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Summary: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].
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2020.124656