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Fundamental solutions and decay rates for evolution problems on the torus \(\mathbb {T}^n\)

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Abstract

In this paper we study large-time behavior evolution problems on the n-dimensional torus \(\mathbb {T}^n\), \(n \ge 1\). Here we analyze the solutions to these problems, studying their regularity and obtaining estimates of them. The main tools we use is the toroidal Fourier transform, together with Fourier series and a version of the Hardy-Littlewood inequality, applied to our case of the n-dimensional torus \(\mathbb {T}^n\). We use this inequality to find an estimate of solutions to evolution problems.

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Acknowledgements

The authors would like to thank the referee for his/her careful reading of the manuscript and constructive suggestions. This work is part of the M.Sc. thesis for the first author.

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  1. Universidad de Concepción, Avda. Esteban Iturra s/n - Barrio Universitario, Concepción, Chile

    Alex Guiñazú & Vicente Vergara

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  1. Alex Guiñazú
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  2. Vicente Vergara
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Correspondence to Alex Guiñazú.

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The authors are partially supported by Fondecyt grant 1190255.

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The authors declare that they have no conflict of interest.

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Guiñazú, A., Vergara, V. Fundamental solutions and decay rates for evolution problems on the torus \(\mathbb {T}^n\). J. Pseudo-Differ. Oper. Appl. 12, 42 (2021). https://doi.org/10.1007/s11868-021-00413-y

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  • DOI: https://doi.org/10.1007/s11868-021-00413-y

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