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Journal Articles Advances in Dynamical Systems and Applications Year : 2009

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

Abstract

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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Dates and versions

hal-00364722 , version 1 (26-02-2009)

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Werner Balser, Michèle Loday-Richaud. Summability of solutions of the heat equation with inhomogeneous thermal conductivity in two variables. Advances in Dynamical Systems and Applications, 2009, 4 (2), pp.159-177. ⟨hal-00364722⟩
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