Blow-up and energy decay for a class of wave equations with nonlocal
Kirchhoff-type diffusion and weak damping
Abstract
The purpose of this paper is to study the following equation driven by a
nonlocal integro-differential operator
$\mathcal{L}_K$:
\[u_{tt}+[u]_s^{2(\theta-1)}\mathcal{L}_Ku+a|u_t|^{m-1}u_t=b|u|^{p-1}u\]
with homogeneous Dirichlet boundary condition and initial data, where
$[u]^2_s$ is the Gagliardo seminorm, $a\geq
0,~b>0,~0
, 
