Published Paper
Inserted: 15 jul 2020
Last Updated: 10 may 2021
Journal: Math. Engineering
Volume: 4
Number: 1
Pages: 1-15
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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