In this paper, we consider discrete semilinear wave equations $\begin{array}{ll}{u}_{tt}\left(x,t\right)={\mathrm{\Delta }}_{\omega }u\left(x,t\right)+f\left(u\left(x,t\right)\right),& \left(x,t\right)\in S\times \left(0,+\mathrm{\infty }\right),\\ u\left(x,t\right)=0,& \left(x,t\right)\in \mathrm{\partial }S\times \left[0,+\mathrm{\infty }\right),\\ u\left(x,0\right)=u_0\left(x\right),u_t\left(x,0\right)=v_0\left(x\right),& x\in S,\end{array}$ where S is a network with boundary $\mathrm{\partial }S$. The main contribution of this work is to introduce a condition $\text{(}C\text{)}\alpha {\int }_0^{u}f\left(s\right)\mathrm{d}s\le uf\left(u\right)+\text{β}{u}^2+\gamma ,u\in \mathbb{R},$ for some $\alpha >2$ and $\text{β},\gamma \ge 0$ with $0\le \text{β}\le \left(\alpha -2\right){\lambda }_0/2$, where ${\lambda }_0$ is the first eigenvalue of discrete Laplacian ${\mathrm{\Delta }}_{\omega }$, and we use the concavity method to obtain the blow-up solutions to the above equations.

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网络上离散半线性波动方程的爆破解的条件

在本文中，我们考虑离散半线性波动方程 uttx , t= Δ ω ux , t + fux , t , x , t ∈ S × 0 , + ∞ , ux , t = 0 , x , t ∈ ∂ S × 0 , + ∞ , ux , 0 = u 0 x , utx , 0 = v 0 x...