A diffusion problem of Kirchhoff type involving the nonlocal fractional p -Laplacian
A diffusion problem of Kirchhoff type involving the nonlocal fractional p -Laplacian
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DOI：
10.3934/dcds.2017171
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发表时间：
2017-04
影响因子：
1.1
通讯作者：
P. Pucci;Mingqi Xiang;Binlin Zhang
中科院分区：
文献类型：
--
作者：
P. Pucci;Mingqi Xiang;Binlin Zhang
In this paper, we study an anomalous diffusion model of Kirchhoff type driven by a nonlocal integro-differential operator. As a particular case, we are concerned with the following initial-boundary value problem involving the fractional $p$-Laplacian $\left\{ \begin{array}{*{35}{l}} {{\partial }_{t}}u+M([u]_{s, p}^{p}\text{)}(-\Delta)_{p}^{s}u=f(x, t) & \text{in }\Omega \times {{\mathbb{R}}^{+}}, {{\partial }_{t}}u=\partial u/\partial t, \\ u(x, 0)={{u}_{0}}(x) & \text{in }\Omega, \\ u=0\ & \text{in }{{\mathbb{R}}^{N}}\backslash \Omega, \\\end{array}\text{ }\ \ \right.$ where $[u]_{s, p}$ is the Gagliardo $p$-seminorm of $u$, $Ω\subset \mathbb{R}^N$ is a bounded domain with Lipschitz boundary $\partialΩ$, $1
