论文标题
具有双功率非线性的半线性热方程的爆炸解决方案存在
Existence of blowup solutions to the semilinear heat equation with double power nonlinearity
论文作者
论文摘要
我们考虑半线性热方程$ u_t =ΔU+| u |^{p-1} u- | u |^{q-1} u $ in $ \ mathbb {r}^n \ times（0，t）$，$ n = 5 $，$ n = 5 $，$ p = = \ frac {n+2} $ n+2} $ n+2} $ q $ q $通过$ - | u |^{q-1} u $的存在，此方程具有有限的时间灭绝属性。我们通过使用此属性来展示一种新型的爆炸解决方案的存在。实际上，我们通过连接$ u_t =ΔU+| U |^{p-1} u $的特定爆炸解决方案以及$ u_t =ΔU-| u | u |^{q-1} u $的特定解决方案来获得此类爆炸解决方案。
We consider the semilinear heat equation $u_t=Δu+|u|^{p-1}u-|u|^{q-1}u$ in $\mathbb{R}^n\times(0,T)$, where $n=5$, $p=\frac{n+2}{n-2}$ and $q\in(0,1)$. By the presence of $-|u|^{q-1}u$, this equation has a finite time extinction property. We show the existence of a new type of blowup solutions by using this property. In fact, we obtain such blowup solutions by connecting a specific blowup solution of $u_t=Δu+|u|^{p-1}u$ and a specific solution of $u_t=Δu-|u|^{q-1}u$, and by adding correction terms.
