In this paper, we explore fractional Kirchhoff-type hyperbolic equations containing logarithmic terms, \(\left \{ \textstyle\begin{array}{l@{\quad}l} u_{tt} +[u]^{2\gamma -2}_{s}(-\Delta )^{s}u+{\left ( { - \Delta } \right )^{s}}{u_{t}}=|u|^{b-2}u\ln \left | u \right |,\ &\text{in } \Omega \times \mathbb{R}^{+}, \\ u(\cdot ,0)=u_{0},\ \ \ \ u_{t}(\cdot ,0)=u_{1},& \text{in } \Omega ,\\ u(x,t)=0,& \text{in } (\mathbb{R}^{N}\setminus \Omega )\times \mathbb{R}^{+}_{0}, \end{array}\displaystyle \right .\) where $[u]_{s}$ is the Gagliardo seminorm of u, $\mathbb{R}_{0}^{+} = \left [ {0, + \infty } \right )$ , $(-\Delta )^{s}$ is the fractional Laplacian operator, $s\in (0,1)$ , $2<2\gamma <b<b+\varepsilon <2_{s}^{*}=\frac{2N}{N-2s}$ for $\varepsilon >0$ , $\Omega \subset \mathbb{R}^{N}$ is a bounded domain with $N>2s$ . Under reasonable assumptions, we study certain properties of solutions to wave equations. By employing the Galerkin method in conjunction with potential well theory, we obtain the global existence of solutions in the subcritical state. Furthermore, using the concavity method and some special inequalities, we prove the asymptotic behavior and blow-up of weak solutions.
