论文标题
多孔介质方程的最佳liouville定理
An optimal Liouville theorem for the porous medium equation
论文作者
论文摘要
在无穷大的敏锐渐近生长条件下，我们证明了对不均匀多孔培养基方程的liouville型定理，只要其普遍接近热方程。此外，对于均匀方程式，我们表明为了得出结论，仅在空间变量中仅假设无穷大的急剧渐近生长就足够了。结果是最佳的，这意味着无穷大的生长条件不能削弱。
Under a sharp asymptotic growth condition at infinity, we prove a Liouville type theorem for the inhomogeneous porous medium equation, provided it stays universally close to the heat equation. Additionally, for the homogeneous equation, we show that for the conclusion to hold, it is enough to assume the sharp asymptotic growth at infinity only in the space variable. The results are optimal, meaning that the growth condition at infinity cannot be weakened.
