论文标题
半线性抛物线方程的琐碎结果
A Triviality Result for Semilinear Parabolic Equations
论文作者
论文摘要
我们在时间上显示了“点”单调的微不足道结果，半线性热方程的“永恒”解决方案\ begin {equation*} u_ {t} =δu + | | | |^{p} \ e |^{p} \ end End {equination {equation*}在$ nne \ ege $ nnne \ egeq $ nnenne \ ege $ nne \ egq perigial nonne \ egq perigial时比关键的sobolev endent $ \ frac {n+2} {n-2} $。
We show a triviality result for "pointwise" monotone in time, bounded "eternal" solutions of the semilinear heat equation \begin{equation*} u_{t}=Δu + |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 $\frac{n+2}{n-2}$.
