Ancient solutions of superlinear heat equations on Riemannian manifolds
Daniele Castorina, Carlo Mantegazza
TL;DR
This paper investigates the qualitative behavior of ancient solutions to superlinear heat equations on Riemannian manifolds, focusing on their positivity and spatial constancy.
Contribution
It provides new insights into the properties of ancient solutions for superlinear heat equations on Riemannian manifolds, emphasizing positivity and spatial uniformity.
Findings
Ancient solutions tend to be positive under certain conditions.
Solutions exhibit spatial constancy in specific scenarios.
The study advances understanding of superlinear heat equations on curved spaces.
Abstract
We study some qualitative properties of ancient solutions of superlinear heat equations on a Riemannian manifold, with particular interest in positivity and constancy in space.
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