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Analyticity in partial differential equations

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Abstract

Here we shall discuss analyticity results for several important partial differential equations. This includes the analytic regularity of sub-Laplacians under the finite type condition; the analyticity of the solution in both variables to the Cauchy problem for the Camassa–Holm equation with analytic initial data by using the Ovsyannikov theorem, which is a Cauchy–Kowalevski type theorem for nonlocal equations; the Cauchy problem for BBM with analytic initial data; the Cauchy problem for KdV with analytic initial data examining the evolution of uniform radius of spatial analyticity; and finally the time regularity of KdV solutions, which is Gevrey 3.

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Acknowledgements

The first author was partially supported by a grant from the Simons Foundation (#524469 to Alex Himonas). The second author was partially supported by Conselho Nacional de Desenvolvimento Científico e Tecnológico—CNPq, Grant 303111/2015-1 and São Paulo Research Foundation (FAPESP), Grant 2018/14316-3. Also, the authors thank the referee for constructive suggestions.

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  1. Department of Mathematics, University of Notre Dame, Notre Dame, IN, 46556, USA

    A. Alexandrou Himonas

  2. Departamento de Matemática, Universidade Federal de São Carlos, São Carlos, SP, 13565-905, Brazil

    Gerson Petronilho

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  1. A. Alexandrou Himonas
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  2. Gerson Petronilho
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Correspondence to A. Alexandrou Himonas.

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In memory of Nick Hanges.

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Himonas, A.A., Petronilho, G. Analyticity in partial differential equations. Complex Anal Synerg 6, 15 (2020). https://doi.org/10.1007/s40627-020-00052-x

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