# A Triviality Result for Semilinear Parabolic Equations

created by root on 15 Jul 2020
modified by catino on 10 May 2021

[BibTeX]

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 $\frac{n+2}{n−2}$.