论文标题
关于与Hilfer-HADAMARD分数衍生物的半线性方程式全球解决方案的不存在
On nonexistence of global solutions for a semilinear equation with Hilfer- Hadamard fractional derivative
论文作者
论文摘要
对于以下半连续方程，使用Hilfer- Hadamard分数衍生\ BEGIN {方程*} \ Mathcal {d}^{α_1，β} _ {a^+} u-Δ\ Mathcal {d} \qquad t>a>0, \qquad x\inΩ, \end{equation*} where $Ω\subset \mathbb{R}^N$ $(N\geqslant 1)$, $p>1$, $0<α_{2}<α_{1}<1$ and $0<β<1$. $ \ Mathcal {d}^{α_i，β} _ {a^+} $ $（i = 1,2）$是订单$α_i$的Hilfer- HADAMARD分数衍生物，我们确定了全球解决方案的必要条件。
For the following semilinear equation with Hilfer- Hadamard fractional derivative \begin{equation*} \mathcal{D}^{α_1,β}_{a^+} u-Δ\mathcal{D}^{α_2,β}_{a^+} u-Δu =\vert u\vert^p, \qquad t>a>0, \qquad x\inΩ, \end{equation*} where $Ω\subset \mathbb{R}^N$ $(N\geqslant 1)$, $p>1$, $0<α_{2}<α_{1}<1$ and $0<β<1$. $\mathcal{D}^{α_i,β}_{a^+}$ $(i=1,2)$ is the Hilfer- Hadamard fractional derivative of order $α_i$ and of type $β$, we establish the necessary conditions for the existence of global solutions.
