We show a triviality result for "pointwise" monotone in time, bounded "eternal" solutions of the semilinear heat equation egin{equation*} u_{t}=Delta u + |u|^{p} end{equation*} on complete Riemannian manifolds of dimension $n geq 5$ with nonnegative Ricci tensor, when $p$ is smaller than the critical Sobolev exponent $rac{n+2}{n-2}$.
A Triviality Result for Semilinear Parabolic Equations / Catino, Giovanni; Castorina, Daniele; Mantegazza, Carlo. - In: MATHEMATICS IN ENGINEERING. - ISSN 2640-3501. - 4:1(2022). [10.3934/mine.2022002]
A Triviality Result for Semilinear Parabolic Equations
Giovanni Catino;Daniele Castorina;Carlo Mantegazza
2022
Abstract
We show a triviality result for "pointwise" monotone in time, bounded "eternal" solutions of the semilinear heat equation egin{equation*} u_{t}=Delta u + |u|^{p} end{equation*} on complete Riemannian manifolds of dimension $n geq 5$ with nonnegative Ricci tensor, when $p$ is smaller than the critical Sobolev exponent $rac{n+2}{n-2}$.File in questo prodotto:
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