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.

Jleli M., Samet B., Vetro C. (2021). A blow-up result for a nonlinear wave equation on manifolds: the critical case. APPLICABLE ANALYSIS, 1-10 [10.1080/00036811.2021.1986026].

A blow-up result for a nonlinear wave equation on manifolds: the critical case

Vetro C.
2021-01-01

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.
2021
Settore MAT/05 - Analisi Matematica
Jleli M., Samet B., Vetro C. (2021). A blow-up result for a nonlinear wave equation on manifolds: the critical case. APPLICABLE ANALYSIS, 1-10 [10.1080/00036811.2021.1986026].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10447/534122
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