论文标题
涉及离散卷积操作员的凯奇分数问题的适应性良好
Well-posedness for Cauchy fractional problems involving discrete convolution operators
论文作者
论文摘要
这项工作的重点是建立足够的条件，以确保以下非线性分数半分化模型的适当性 \ begin {equation*} \ begin {case} \ mathbb d^β_tu（n，t）= b u（n，t） + f（n-ct，u（n，t）），\＆n \ in \ mathbb {z}，\; t> 0， u（n，0）=φ（n），\; ＆n \ in \ mathbb {z}， \ end {cases} \ end {equation*} 在假设（0,1] $中的$β\，$ c> 0 $的某些常数，$ b $是一个离散的卷积运算符，带有内核$ b \ in \ ell^1（\ z）$，这是Markovian $ C_0 $的无限发电机，以及适当的非线性$ f $。解决方案原理根据各自的初始值。
This work is focused on establishing sufficient conditions to guarantee the well-posedness of the following nonlinear fractional semidiscrete model \begin{equation*} \begin{cases} \mathbb D^β_t u(n,t)= B u(n,t) + f(n-ct,u(n,t)),\, &n\in\mathbb{Z}, \;t>0, u(n,0)=φ(n),\; &n\in\mathbb{Z}, \end{cases} \end{equation*} under the assumptions that $β\in (0,1]$, $c>0$ some constant, $B$ is a discrete convolution operator with kernel $b\in\ell^1(\Z)$, which is the infinitesimal generator of the Markovian $C_0$-semigroup and suitable nonlinearity $f$. We present results concerning the existence and uniqueness of solution, as well as establishing a comparison principle of solutions according to respective initial values.
