On Borel summable solutions of the multidimensional heat equation

Volume 105 / 2012

Sławomir Michalik Annales Polonici Mathematici 105 (2012), 167-177 MSC: 35K05, 35C10. DOI: 10.4064/ap105-2-5


We give a new characterisation of Borel summability of formal power series solutions to the $n$-dimensional heat equation in terms of holomorphic properties of the integral means of the Cauchy data. We also derive the Borel sum for the summable formal solutions.


  • Sławomir MichalikInstitute of Mathematics
    Polish Academy of Sciences
    P.O. Box 21, Śniadeckich 8
    00-956 Warszawa, Poland
    Faculty of Mathematics and Natural Sciences
    College of Science
    Cardinal Stefan Wyszyński University
    Wóycickiego 1/3
    01-938 Warszawa, Poland

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