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A Triviality Result for Semilinear Parabolic Equations

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 نشر من قبل Giovanni Catino
 تاريخ النشر 2020
  مجال البحث
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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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