# A Triviality Result for Semilinear Parabolic Equations

created by root on 15 Jul 2020
modified on 18 Feb 2021

[BibTeX]

Accepted Paper

Inserted: 15 jul 2020
Last Updated: 18 feb 2021

Journal: Math. Engineering
Year: 2020

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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