论文标题
分层谎言组的富士
Fujita exponent on stratified Lie groups
论文作者
论文摘要
我们证明，$ \ frac {q} {q-2} $是与均匀尺寸$ q $的任意分层的谎言组上半线性加热方程的富吉塔指数。这涵盖了欧几里得的案例，并对尼尔氏谎言群体的证明技术提供了新的见解。我们研究的方程式具有强迫术语，仅取决于组元素，并且具有积极的积分。分层的谎言组结构以及测试功能方法和Banach固定点定理在我们的证明中起着重要作用。
We prove that $\frac{Q}{Q-2}$ is the Fujita exponent for a semilinear heat equation on an arbitrary stratified Lie group with homogeneous dimension $Q$. This covers the Euclidean case and gives new insight into proof techniques on nilpotent Lie groups. The equation we study has a forcing term which depends only upon a group element and has positive integral. The stratified Lie group structure plays an important role in our proofs, along with test function method and Banach fixed point theorem.
