Divergent solutions of the heat equation: On an article of Lutz, Miyake and Schäfke
Werner Balser · Pacific Journal of Mathematics · 1999
In this article, we generalize results of Lutz, Miyake and Schäfke concerning summability of formal solutions of the Cauchy problem for the complex heat equation. In particular, we show that the type of summability depends on the given initial condition. 0. Introduction. In detail, we will be concerned with the following problem for the complex heat equation (in two complex variables τ and z): (0.1) uτ (τ,z)=uzz(τ,z), u(0,z) = ˆϕ(z),