A blow-up result for a nonlinear wave equation on manifolds: the critical case
- Authors: Jleli M.; Samet B.; Vetro C.
- Publication year: 2023
- Type: Articolo in rivista
- OA Link: http://hdl.handle.net/10447/534122
Abstract
We consider a inhomogeneous semilinear wave equation on a noncompact complete Riemannian manifold (Formula presented.) of dimension (Formula presented.), 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 (Formula presented.), our result improves the existing literature. Namely, our main result is valid without assuming that the initial values are compactly supported.