×

Formal power series solutions of the heat equation in one spatial variable. (English) Zbl 1356.35118

Bertrand, Daniel (ed.) et al., Differential equations and quantum groups. Andrey A. Bolibrukh memorial volume. Zürich: European Mathematical Society Publishing House (ISBN 3-03719-020-5/pbk). IRMA Lectures in Mathematics and Theoretical Physics 9, 49-58 (2007).
Summary: We investigate formal power series solutions of the heat equation in one spatial variable. In previous work of D. A. Lutz et al. [Nagoya Math. J. 154, 1–29 (1999; Zbl 0958.35061)] and of the author, solutions of the Cauchy problem have been shown to be \(k\)-summable in a direction \(d\) if and only if the initial condition satisfies a certain condition. Here, we investigate the initial value problem for the spatial variable, finding new results especially for the case in which the initial values are Gevrey functions of order larger than one, so that the corresponding power series solution diverges.
For the entire collection see [Zbl 1104.00017].

MSC:

35K05 Heat equation
35C10 Series solutions to PDEs

Citations:

Zbl 0958.35061
PDFBibTeX XMLCite
Full Text: DOI