Well-posedness and asymptotic behavior for the dissipative $p$-biharmonic wave equation with logarithmic nonlinearity and damping terms

This paper concerns with the initial and boundary value problem for a $p$-biharmonic wave equation with logarithmic nonlinearity and damping terms. We establish the well-posedness of the global solution by combining Faedo–Galerkin approximation and the potential well method, and derive both the polynomial and exponential energy decay by introducing an appropriate Lyapunov functional. Moreover, we use the technique of differential inequality to obtain the blow-up conditions and deduce the life-span of the blow-up solution.