A triviality result for semilinear parabolic equations
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, whe...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2022-01-01
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| Series: | Mathematics in Engineering |
| Subjects: | |
| Online Access: | https://aimspress.com/article/doi/10.3934/mine.2022002?viewType=HTML |
| Summary: | 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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| ISSN: | 2640-3501 |