Abstract This paper deals with a class of nonlocal semilinear pseudo-parabolic equation with conical degeneration u t − △ B u t − △ B u = | u | p − 1 u − 1 | B | ∫ B | u | p − 1 u d x 1 x 1 d x ′ , on a manifold with conical singularity, where △ B is Fuchsian type Laplace operator with totally characteristic degeneracy on the boundary x 1 = 0 . By using the modified method of potential well with Galerkin approximation and concavity, the global existence, uniqueness, finite time blow up and asymptotic behavior of the solutions will be discussed at the low initial energy J ( u 0 ) d and critical initial energy J ( u 0 ) = d , respectively. Furthermore, we investigate the global existence and finite time blow up of the solutions with the high initial energy J ( u 0 ) > d by the variational method. Especially, we also derive the threshold results of global existence and nonexistence for the solutions at two different initial energy levels, i.e. low initial level and critical initial level.

中文翻译：

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具有圆锥退化的非局部半线性伪抛物线方程的全局适定性

摘要 本文研究一类具有圆锥退化的非局部半线性伪抛物线方程 ut − △ B ut − △ B u = | 你| p − 1 u − 1 | 乙 | ∫ B | 你| p − 1 udx 1 x 1 dx ′ ，在圆锥奇点的流形上，其中 △ B 是 Fuchsian 型拉普拉斯算子，在边界 x 1 = 0 上具有完全特征简并。利用Galerkin近似和凹面的改进势阱方法，讨论了在低初始能量J ( u 0 ) d 和临界初始能量J ( u 0 ) = d 分别。此外，我们通过变分方法研究了具有高初始能量 J ( u 0 ) > d 的解的全局存在性和有限时间爆炸。尤其，