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arXiv · 2007.07655

A Triviality Result for Semilinear Parabolic Equations

Giovanni Catino·Daniele Castorina·Carlo Mantegazza
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Abstract

We show a triviality result for "pointwise" monotone in time, bounded "eternal" solutions of the semilinear heat equation \begin{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 $\frac{n+2}{n-2}$.

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Giovanni Catino, Daniele Castorina, Carlo Mantegazza. 2020-07-15. A Triviality Result for Semilinear Parabolic Equations. https://arxiv.org/abs/2007.07655

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