A Lyapunov functional and blow-up results for a class of perturbations for semilinear wave equations in the critical case

Details A Lyapunov functional and blow-up results for a class of perturbations for semilinear wave equations in the critical case A Lyapunov functional and blow-up results for a class of perturbations for semilinear wave equations in the critical case

2010-05-20

arxiv.org/abs/1005.3771v2

Mathematics

Analysis of PDEs

27 pages

Scientific paper

We consider in this paper some class of perturbation for the semilinear wave equation with critical (in the conformal transform sense) power nonlinearity. Working in the framework of similarity variables, we find a Lyapunov functional for the problem. Using a two-step argument based on interpolation and a critical Gagliardo-Nirenberg inequality, we show that the blow-up rate of any sigular solution is given by the solution of the non perturbed associated ODE, namely $u" = u^p$.

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