In this paper, we revisit the following nonlocal Kirchhoff diffusion problem:∂tu+M([u]s2)LKu=|u|p−2u,inΩ×R+,u(x,t)=0,in(RN\Ω)×R+,u(x,0)=u0(x),inΩ,where ##IMG## [http://ej.iop.org/images/0951-7715/33/11/6099/nonab9f84ieqn2.gif] {${\Omega}\subset {\mathbb{R}}^{N}$} is a bounded domain with Lipschitz boundary, [ u ] s is the Gagliardo seminorm of u , 0 < s < min{1, N /2}, ##IMG## [http://ej.iop.org/images/0951-7715/33/11/6099/nonab9f84ieqn3.gif] {${\mathcal{L}}_{K}$} is a nonlocal integro-differential operator defined in (1.2), which generalizes the fractional Laplace operator (−Δ) s , u 0 : Ω → [0, +∞) is the initial function, M : [0, +∞) → [0, +∞) is a continuous function and there exist two constants θ > 1 and m 0 > 0 such thatM(σ)⩾m0σθ−1,∀σ∈[0,+∞).This problem has been investigated by Xiang, Rădulescu and Zhang in...

中文翻译：

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一个非局部Kirchhoff扩散问题的解的整体存在和爆炸

在本文中，我们重新审视以下非局部Kirchhoff扩散问题：∂tu+ M（[s] s2）LKu = | u | p-2u，inΩ×R +，u（x，t）= 0，in（RN \Ω ）×R +，u（x，0）= u0（x），inΩ，其中## IMG ## [http://ej.iop.org/images/0951-7715/33/11/6099/nonab9f84ieqn2.gif ] {$ {\ Omega} \ subset {\ mathbb {R}} ^ {N} $}是一个具有Lipschitz边界的有界域，[u] s是u的Gagliardo半范数，0 <s <min {1，N / 2}，## IMG ## [http://ej.iop.org/images/0951-7715/33/11/6099/nonab9f84ieqn3.gif] {$ {\ mathcal {L}} _ {K} $ }是（1.2）中定义的非局部积分微分算子，它推广了分数拉普拉斯算子（-Δ）s，u 0：Ω→[0，+∞）是初始函数，M：[0，+∞） →[0，+∞）是一个连续函数，并且存在两个常数θ> 1和m 0> 0，从而M（σ）⩾m0σθ−1，∀σ∈[0，+∞）。向，拉杜列斯库和张在...