The Blow-Up Rate for Strongly Perturbed Semilinear Wave Equations

We consider in this paper a large class of perturbed semilinear wave equation with subconformal power nonlinearity. In particular, we allow log perturbations of the main source. We derive a Lyapunov functional in similarity variables and use it to derive the blow-up rate. Throughout this work, we use some techniques developped for the unperturbed case studied by Merle and Zaag (Int. Math. Res. Notices, 19(1):1127-1156, 2005) together with ideas introduced by Hamza and Zaag in (Nonlinearity, 25(9):2759-2773, 2012) for a class of perturbations.