Lifespan estimates and asymptotic stability for a class of fourth-order damped p-Laplacian wave equations with logarithmic nonlinearity

In this study, we investigate a damped p-Laplacian wave equation with logarithmic nonlinearity, given byu(tt )+ Delta(2)u - Delta(p)u + (g * Delta u)(t) - Delta u(t )+ eta(t)u(t )= |u|(gamma-2 )u ln |u| in Omega x R+,where gamma > p > 2 and Omega subset of R-n. By making appropriate assumptions on the relaxation function g and the initial data, we establish the occurrence of finite time blow-up for solutions at varying initial energy levels. For sub-critical initial energy, we obtain blow-up solutions within the framework of potential wells in combination with concavity arguments. We also demonstrate that under suitable conditions, solutions with arbitrarily high positive initial energy will blow up. Furthermore, we discuss lifespan estimates for blowing up solutions. In addition, we provide a general stability analysis of the solution energy. Our results in this work complement and extend the previous work of Pereira et al. (Math Methods Appl Sci 46:8831-8854, 2023) in which the blow-up and decay results were obtained for the case gamma = p.