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Hyperasymptotic Solutions for Certain Partial Differential Equations

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Formal and Analytic Solutions of Diff. Equations (FASdiff 2017)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 256))

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Abstract

We present the hyperasymptotic expansions for a certain group of solutions of the heat equation. We extend this result to a more general case of linear PDEs with constant coefficients. The generalization is based on the method of Borel summability, which allows us to find integral representations of solutions for such PDEs.

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Acknowledgements

The authors would like to thank the anonymous referee for valuable comments, suggestions, and especially for indication of the form of hyperasymptotic expansion of the solution u(t, z) presented in (16).

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Authors and Affiliations

  1. Faculty of Mathematics and Natural Sciences, College of Science, Cardinal Stefan Wyszyński University, Wóycickiego 1/3, 01-938, Warszawa, Poland

    Sławomir Michalik & Maria Suwińska

Authors
  1. Sławomir Michalik
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  2. Maria Suwińska
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Corresponding author

Correspondence to Sławomir Michalik .

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Editors and Affiliations

  1. Institute of Mathematics, University of Warsaw, Warsaw, Poland

    Galina Filipuk

  2. Departamento de Física y Matemáticas, University of Alcalá, Alcalá de Henares, Spain

    Alberto Lastra

  3. Faculty of Mathematics and Natural Sciences, College of Science, Cardinal Stefan Wyszynski University, Warsaw, Poland

    Sławomir Michalik

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Michalik, S., Suwińska, M. (2018). Hyperasymptotic Solutions for Certain Partial Differential Equations. In: Filipuk, G., Lastra, A., Michalik, S. (eds) Formal and Analytic Solutions of Diff. Equations . FASdiff 2017. Springer Proceedings in Mathematics & Statistics, vol 256. Springer, Cham. https://doi.org/10.1007/978-3-319-99148-1_4

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