Lyapunov functional and blow-up results for a class of perturbed semilinear wave equations in the critical case
Résumé
We study a class of perturbations for the semilinear wave equation with critical power nonlinearity (in the conformal transform sense). Working in the framework of similarity variables, we introduce a Lyapunov functional for this problem. Using a two-step argument based on interpolation and a critical Gagliardo–Nirenberg inequality, we establish that the blow-up rate of any singular solution is given by the solution of the nonperturbed associated ODE, specifically u″ = u p .