A blow-up result for a nonlinear wave equation on manifolds: the critical case. Issue 5 (24th March 2023) - Jleli, Mohamed; Samet, Bessem; Vetro, Calogero
Abstract : We consider a inhomogeneous semilinear wave equation on a noncompact complete Riemannian manifold ( M, g ) of dimension N ≥ 3, without boundary. The reaction exhibits the combined effects of a critical term and of a forcing term. Using a rescaled test function argument together with appropriate estimates, we show that the equation admits no global solution. Moreover, in the special case when M = R 3, our result improves the existing literature. Namely, our main result is valid without assuming that the initial values are compactly supported.