*Published Paper*

**Inserted:** 15 jul 2020

**Last Updated:** 23 jan 2022

**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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