论文标题
具有衍生物类型非线性的广义三角素方程的爆炸结果
A blow-up result for a generalized Tricomi equation with nonlinearity of derivative type
论文作者
论文摘要
在此注释中，我们证明了半连通的Tricomi方程的爆炸结果，其非线性类型的术语，即方程$ \ Mathscr {t} _ {\！\！\！\！\！\！\！\！\！\！ \ partial_t^2-t^{2 \ ell}δ$。当非线性术语的指数$ p $低于$ \ frac {\ mathscr {Q}}} {\ Mathscr {Q} -2} $时，平滑的解决方案在有限的时间内获取正面的cauchy数据，其中$ \ nathscr {Q}} $，其中$ \ MATHSCR {Q} =（Q} =（Q} =（Q} =（Ell+1）N+1） $ \ mathscr {t} _ {\！\！\ ell} $。此外，我们还获得了寿命的上限估计。
In this note, we prove a blow-up result for a semilinear generalized Tricomi equation with nonlinear term of derivative type, i.e., for the equation $\mathscr{T}_{\!\!\ell} u = |\partial_t u|^p$, where $ \mathscr{T}_{\!\!\ell} = \partial_t^2-t^{2\ell}Δ$. Smooth solutions blow up in finite time for positive Cauchy data when the exponent $p$ of the nonlinear term is below $\frac{\mathscr{Q}}{\mathscr{Q}-2}$, where $\mathscr{Q}=(\ell+1)n+1$ is the quasi-homogeneous dimension of the generalized Tricomi operator $\mathscr{T}_{\!\!\ell}$. Furthermore, we get also an upper bound estimate for the lifespan.
