Published Paper
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Inserted: 15 jul 2020
Last Updated: 9 nov 2026

Journal: Math. Engineering
Volume: 4
Number: 1
Pages: Paper n.002, 15 pp.
Year: 2022

Abstract:

We show a triviality result for “pointwise” monotone in time, bounded “eternal” solutions of the semilinear heat equation $u_t=∆u+
u
^p$ on complete Riemannian manifolds of dimension $n\geq5$ with nonnegative Ricci tensor, when $p$ is smaller than the critical Sobolev exponent $\frac{n+2}{n−2}$.

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