Fujita-type results for the degenerate parabolic equations on the Heisenberg groups
Fujita-type results for the degenerate parabolic equations on the Heisenberg groups
复制标题
DOI：
10.1007/s00030-023-00907-2
复制
发表时间：
2023-03
期刊：
影响因子：
--
通讯作者：
A. Fino;Michael Ruzhansky;B. Torebek
中科院分区：
文献类型：
--
作者：
A. Fino;Michael Ruzhansky;B. Torebek
在本文中，我们考虑具有幂律非线性的海森堡群上的简并抛物型方程的柯西问题。我们获得藤田型临界指数，它取决于海森堡群的齐次维数。分析包括多孔介质方程的情况。我们的证明方法基于专门适应海森堡群性质的非线性容量估计方法。我们还将卡普兰本征函数方法与海森堡群上的 Hopf 型引理结合使用。
In this paper, we consider the Cauchy problem for the degenerate parabolic equations on the Heisenberg groups with power law non-linearities. We obtain Fujita-type critical exponents, which depend on the homogeneous dimension of the Heisenberg groups. The analysis includes the case of porous medium equations. Our proof approach is based on methods of nonlinear capacity estimates specifically adapted to the nature of the Heisenberg groups. We also use the Kaplan eigenfunctions method in combination with the Hopf-type lemma on the Heisenberg groups.