论文标题
半线性热方程式的富士式指数，并在海森堡组上迫使术语
The Fujita exponent for a semilinear heat equation with forcing term on Heisenberg Group
论文作者
论文摘要
在本文中，我们研究了Heisenberg组的强迫术语的半线性热方程式的关键指数。我们的证明技术是基于特异性适应海森伯格集团本质的非线性容量估计方法的方法。令人惊讶的是，与欧几里得案相反，在海森伯格组的所有维度上，关键指数将受到界定，而欧几里得案将是无限的。此外，我们对局部溶液的寿命进行了上限估计。
In this paper, we study a critical exponent to the semilinear heat equation with forcing term on Heisenberg group. Our technique of proof is based on methods of nonlinear capacity estimates specifically adapted to the nature of the Heisenberg group. Surprisingly, the critical exponent will be bounded for all dimensions of the Heisenberg group, in contrast to the Euclidean case which in the 1D and 2D cases will be infinite. In addition, we give an upper bound estimate on the lifespan of local solutions.
