Summability of solutions of the heat equation with inhomogeneous thermal conductivity in two variables

Details Summability of solutions of the heat equation with inhomogeneous thermal conductivity in two variables Summability of solutions of the heat equation with inhomogeneous thermal conductivity in two variables

2009-02-27

arxiv.org/abs/0902.4843v1

Advances in Dynamical Systems and Applications 4, 2 (2009) 159-177

Mathematics

Dynamical Systems

16 pages

Scientific paper

We investigate Gevrey order and 1-summability properties of the formal solution of a general heat equation in two variables. In particular, we give necessary and sufficient conditions for the 1-summability of the solution in a given direction. When restricted to the case of constants coefficients, these conditions coincide with those given by D.A. Lutz, M. Miyake, R. Schaefke in a 1999 article, and we thus provide a new proof of their result.

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