A blow-up result for a nonlinear wave equation on manifolds: the critical case. Issue 5 (24th March 2023)

• Record Type: Journal Article
• Authors: Jleli, Mohamed; Samet, Bessem; Vetro, Calogero
• Is Part Of: Applicable analysis. Volume 102:Issue 5(2023)
• Page Start: 1463
• Page End: 1472
• Publication Date: 2023-03-24
• Subjects: Blow-up -- inhomogeneous semilinear wave equation -- critical case -- manifold; 35B44 -- 35B33; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2021.1986026
• Languages: English
• ISSNs: 0003-6811

Abstract

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.