论文标题
Heisenberg Group上全球解决方案全球解决方案的不存在结果
Nonexistence results of global solutions for fractional order integral equations on the Heisenberg group
论文作者
论文摘要
我们使用时间非局部非线性$$^{c} \ MATHBF {d} _ {0 \ mid t}^ββ\ left（u \ right） +\ left（-Δ_ {\ mathbb { \ frac {1} {γ（α）} \ int_ {0}^{t} \ left（t-ω\ right）^{α-1} \ vert u（ω）\ vert u（ω）\ vert^{p}dΩ数据$ u（。，0）= u_ {0}（。）$，其中$ m> 1 \，\ p> 1 \，\ 0 <β<β<1 \，\ 0 <α<1 $，以及$^{c} \ a {c} \ mathbf {d} _ {d} _ {0 \ hid t} t}^$ deriv fractiv fractiv fractiv fractiv fractiv fractiv fractiv $δ_ {\ Mathbb {h}} $是$（2N+1）$二维的Heisenberg $ \ Mathbb {h} $上的laplacian操作员。
We consider the fractional order integral equation with a time nonlocal nonlinearity $$^{c}\mathbf{D}_{0\mid t}^β\left( u \right) +\left(-Δ_{\mathbb{H}} \right)^{m} \left( u \right) = \frac{1}{Γ(α)}\int_{0}^{t}\left( t-ω\right)^{α-1}\vert u(ω)\vert^{p} dω,$$ posed in $ (.,t)\in\mathbb{H}\times(0,\infty) $, supplemented with an initial data $u(.,0)=u_{0}(.) $,where $ m>1 \ , \ p>1 \ , \ 0<β<1 \ , \ 0<α<1 $, and $^{c}\mathbf{D}_{0\mid t}^β $ denotes the caputo fractional derivative of order $ β$, and $Δ_{\mathbb{H}}$ is the Laplacian operator on the $ (2N+1) $-dimensional Heisenberg group $\mathbb{H} $.Then, we prove a blow up result for its solutions.
