A triviality result for semilinear parabolic equations
نویسندگان
چکیده
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 dimension n \geq 5 with nonnegative Ricci tensor, when p is smaller than critical Sobolev exponent \frac{n+2}{n-2} $.
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ژورنال
عنوان ژورنال: Mathematics in engineering
سال: 2022
ISSN: ['2640-3501']
DOI: https://doi.org/10.3934/mine.2022002