We study the qualitative properties of ancient solutions of linear and semilinear heat equations in a Riemannian manifold, with particular attention to positivity and constancy in space.
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Daniele Castorina, Carlo Mantegazza, Ancient solutions of semilinear heat equations on Riemannian manifolds. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 28 (2017), no. 1, pp. 85–101DOI 10.4171/RLM/753