This paper focuses on the investigation of a hyperbolic Kirchhoff equation with nonlinear damping and higher-order dissipation terms. Initially, the existence and uniqueness of local weak solutions are rigorously established. Next, within the framework of potential well theory, the classification of solution behaviors, including blow-up and global existence, is systematically analyzed according to the relationships among the exponents of nonlinear source terms. Finally, explicit bounds for the blow-up time and decay estimates for global solutions are presented.

This paper focuses on the investigation of a hyperbolic Kirchhoff equation with nonlinear damping and higher-order dissipation terms. Initially, the existence and uniqueness of local weak solutions are rigorously established. Next, within the framework of potential well theory, the classification of solution behaviors, including blow-up and global existence, is systematically analyzed according to the relationships among the exponents of nonlinear source terms. Finally, explicit bounds for the blow-up time and decay estimates for global solutions are presented.